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<!DOCTYPE html><html lang="en">
<head>
<meta charset="utf-8"/>
<title>List of sorting networks</title>
<meta name = "keywords" content = "Sorting networks, list" />
<meta name = "description" content = "Smallest and fastest sorting networks for a given number of inputs" />
<meta name = "author" content = "Bert Dobbelaere" />
<link rel="icon" href="sorticon32.png" sizes="32x32">
<style>
body {
background-color: linen;
}
table {
border-collapse: collapse;
}
table, th, td {
border: 1px solid black;
}
th {
background-color: rgb(120,150,255);
padding: 10px 20px 10px 20px;
}
td {
padding: 20px 20px 20px 20px;
}
td.idx {
padding: 2px 20px 2px 20px;
}
h2 {
padding: 50px 50px 30px 50px;
}
p.mono {
font-family: "Lucida Console", monospace;
font-size: 80%;
color: rgb(0,80,150);
}
</style>
</head><body>
<h2>Smallest and fastest sorting networks for a given number of inputs</h2>
<p>Below are the best performing <a href="https://en.wikipedia.org/wiki/Sorting_network">sorting networks</a> known by the author for network sizes of up to 64 inputs, in terms of two metrics:<br>
<ul><li>Number of compare/exchange elements (CEs) - metric below called "size"</li>
<li>Number of parallel operation steps (layers), determining processing latency - metric below called "depth"</li></ul>
<p>Provided is a minimum set of networks that each can be the best choice depending on how both criteria are weighted.</p>
<p>If no source is mentioned, the network was generated by the <a href="https://github.com/bertdobbelaere/SorterHunter">SorterHunter</a> program, which in many cases matches or outperforms pre-existing networks.</p>
<p>For a number of input sizes (n), the used method was able to reduce the upper bound for the minimal network size S(n) compared to the results reported by V. Valsalam & R. Miikkulainen [<a href="#VM13">VM13</a>].<br>
This was the case for 18…23 inputs. For 24…29, 33…48 and 54…56 inputs, a reduction was achieved vs. the Batcher odd-even and Van Voorhis (4,4) merges of smaller networks.</p><p>For 25 and 26 inputs, a reduction in depth was achieved vs. the Batcher odd-even merge of smaller networks, lowering the optimal depth upper bound to 13 layers. For 34 inputs, a similar reduction in depth to 15 layers was achieved, and for 42…44 inputs a reduction to 17 layers.</p>
<p>For questions, remarks, or to contribute improved results please contact bert.o.dobbelaere[at]telenet[dot]be.</p><p>For a reduced version of this page, see the <a href="sorting_networks.html">list of sorting networks up to 32 inputs</a></p><h3>Summary table</h3>
<table><tr><th>Number of inputs</th><th>(Size,Depth) combinations</th><th>Min. size bounds<br><a href="https://oeis.org/A003075">OEIS A003075</a></th><th>Min. depth bounds<br><a href="https://oeis.org/A067782">OEIS A067782</a></th><th>Comments</th></tr>
<tr><td class="idx">2</td><td class="idx"><a href="#N2L1D1">(1, 1)</a> </td><td class="idx"><b>1</b></td><td class="idx"><b>1</b></td><td class="idx">Trivial</td></tr>
<tr><td class="idx">3</td><td class="idx"><a href="#N3L3D3">(3, 3)</a> </td><td class="idx"><b>3</b></td><td class="idx"><b>3</b></td><td class="idx">[<a href="#TAOCPv3">TAOCPv3</a>]</td></tr>
<tr><td class="idx">4</td><td class="idx"><a href="#N4L5D3">(5, 3)</a> </td><td class="idx"><b>5</b></td><td class="idx"><b>3</b></td><td class="idx">[<a href="#TAOCPv3">TAOCPv3</a>]</td></tr>
<tr><td class="idx">5</td><td class="idx"><a href="#N5L9D5">(9, 5)</a> </td><td class="idx"><b>9</b></td><td class="idx"><b>5</b></td><td class="idx">[<a href="#TAOCPv3">TAOCPv3</a>]</td></tr>
<tr><td class="idx">6</td><td class="idx"><a href="#N6L12D5">(12, 5)</a> </td><td class="idx"><b>12</b></td><td class="idx"><b>5</b></td><td class="idx">[<a href="#TAOCPv3">TAOCPv3</a>]</td></tr>
<tr><td class="idx">7</td><td class="idx"><a href="#N7L16D6">(16, 6)</a> </td><td class="idx"><b>16</b></td><td class="idx"><b>6</b></td><td class="idx">[<a href="#TAOCPv3">TAOCPv3</a>]</td></tr>
<tr><td class="idx">8</td><td class="idx"><a href="#N8L19D6">(19, 6)</a> </td><td class="idx"><b>19</b></td><td class="idx"><b>6</b></td><td class="idx">[<a href="#TAOCPv3">TAOCPv3</a>]</td></tr>
<tr><td class="idx">9</td><td class="idx"><a href="#N9L25D7">(25, 7)</a> </td><td class="idx"><b>25</b></td><td class="idx"><b>7</b></td><td class="idx">[<a href="#TAOCPv3">TAOCPv3</a>], Optimal depth proven in [<a href="#Par89">Par89</a>], optimal size proven in [<a href="#CCFS16">CCFS16</a>]</td></tr>
<tr><td class="idx">10</td><td class="idx"><a href="#N10L29D8">(29, 8)</a> <a href="#N10L31D7">(31, 7)</a> </td><td class="idx"><b>29</b></td><td class="idx"><b>7</b></td><td class="idx">[<a href="#TAOCPv3">TAOCPv3</a>], Optimal depth proven in [<a href="#Par89">Par89</a>], optimal size proven in [<a href="#CCFS16">CCFS16</a>]</td></tr>
<tr><td class="idx">11</td><td class="idx"><a href="#N11L35D8">(35, 8)</a> </td><td class="idx"><b>35</b></td><td class="idx"><b>8</b></td><td class="idx">[<a href="#TAOCPv3">TAOCPv3</a>], Optimal depth proven in [<a href="#BZ14">BZ14</a>], optimal size proven by [<a href="#Harder19">Harder19</a>]</td></tr>
<tr><td class="idx">12</td><td class="idx"><a href="#N12L39D9">(39, 9)</a> <a href="#N12L40D8">(40, 8)</a> </td><td class="idx"><b>39</b></td><td class="idx"><b>8</b></td><td class="idx">[<a href="#TAOCPv3">TAOCPv3</a>], Optimal depth proven in [<a href="#BZ14">BZ14</a>], optimal size proven by [<a href="#Harder19">Harder19</a>]</td></tr>
<tr><td class="idx">13</td><td class="idx"><a href="#N13L45D10">(45, 10)</a> <a href="#N13L46D9">(46, 9)</a> </td><td class="idx">43…45</td><td class="idx"><b>9</b></td><td class="idx">[<a href="#TAOCPv3">TAOCPv3</a>], Optimal depth proven in [<a href="#BZ14">BZ14</a>]</td></tr>
<tr><td class="idx">14</td><td class="idx"><a href="#N14L51D10">(51, 10)</a> <a href="#N14L52D9">(52, 9)</a> </td><td class="idx">47…51</td><td class="idx"><b>9</b></td><td class="idx">[<a href="#TAOCPv3">TAOCPv3</a>], Optimal depth proven in [<a href="#BZ14">BZ14</a>]</td></tr>
<tr><td class="idx">15</td><td class="idx"><a href="#N15L56D10">(56, 10)</a> <a href="#N15L57D9">(57, 9)</a> </td><td class="idx">51…56</td><td class="idx"><b>9</b></td><td class="idx">[<a href="#TAOCPv3">TAOCPv3</a>], Optimal depth proven in [<a href="#BZ14">BZ14</a>]</td></tr>
<tr><td class="idx">16</td><td class="idx"><a href="#N16L60D10">(60, 10)</a> <a href="#N16L61D9">(61, 9)</a> </td><td class="idx">55…60</td><td class="idx"><b>9</b></td><td class="idx">[<a href="#TAOCPv3">TAOCPv3</a>], Optimal depth proven in [<a href="#BZ14">BZ14</a>]</td></tr>
<tr><td class="idx">17</td><td class="idx"><a href="#N17L71D12">(71, 12)</a> <a href="#N17L72D11">(72, 11)</a> <a href="#N17L74D10">(74, 10)</a> </td><td class="idx">60…71</td><td class="idx"><b>10</b></td><td class="idx">Size ubound: [<a href="#Baddar09">Baddar09</a>], depth ubound: [<a href="#EM14">EM14</a>], depth optimality: [<a href="#CCEMS16">CCEMS16</a>]</td></tr>
<tr><td class="idx">18</td><td class="idx"><a href="#N18L77D12">(77, 12)</a> <a href="#N18L78D11">(78, 11)</a> </td><td class="idx">65…77</td><td class="idx">10…11</td><td class="idx">Size ubound: <a href="https://github.com/bertdobbelaere/SorterHunter">SorterHunter</a>, depth ubound: [<a href="#Baddar09">Baddar09</a>]</td></tr>
<tr><td class="idx">19</td><td class="idx"><a href="#N19L85D12">(85, 12)</a> <a href="#N19L87D11">(87, 11)</a> </td><td class="idx">70…85</td><td class="idx">10…11</td><td class="idx">Size ubound: <a href="https://github.com/bertdobbelaere/SorterHunter">SorterHunter</a>, depth ubound: [<a href="#EM14">EM14</a>].</td></tr>
<tr><td class="idx">20</td><td class="idx"><a href="#N20L91D12">(91, 12)</a> <a href="#N20L93D11">(93, 11)</a> </td><td class="idx">75…91</td><td class="idx">10…11</td><td class="idx">Size ubound: <a href="https://github.com/bertdobbelaere/SorterHunter">SorterHunter</a>, depth ubound: [<a href="#EM14">EM14</a>].</td></tr>
<tr><td class="idx">21</td><td class="idx"><a href="#N21L99D15">(99, 15)</a> <a href="#N21L100D12">(100, 12)</a> </td><td class="idx">80…99</td><td class="idx">10…12</td><td class="idx">Size ubound: <a href="https://github.com/bertdobbelaere/SorterHunter">SorterHunter</a>, depth ubound: [<a href="#Baddar09">Baddar09</a>]</td></tr>
<tr><td class="idx">22</td><td class="idx"><a href="#N22L106D13">(106, 13)</a> <a href="#N22L107D12">(107, 12)</a> </td><td class="idx">85…106</td><td class="idx">10…12</td><td class="idx">Size ubound: <a href="https://github.com/bertdobbelaere/SorterHunter">SorterHunter</a>, depth ubound: [<a href="#Baddar09">Baddar09</a>]</td></tr>
<tr><td class="idx">23</td><td class="idx"><a href="#N23L114D14">(114, 14)</a> <a href="#N23L115D13">(115, 13)</a> <a href="#N23L116D12">(116, 12)</a> </td><td class="idx">90…114</td><td class="idx">10…12</td><td class="idx">Size ubound: <a href="https://github.com/bertdobbelaere/SorterHunter">SorterHunter</a>, depth ubound: [<a href="#Ehlers17">Ehlers17</a>]</td></tr>
<tr><td class="idx">24</td><td class="idx"><a href="#N24L120D13">(120, 13)</a> <a href="#N24L122D12">(122, 12)</a> </td><td class="idx">95…120</td><td class="idx">10…12</td><td class="idx">Size ubound: <a href="https://github.com/bertdobbelaere/SorterHunter">SorterHunter</a>, depth ubound: [<a href="#Ehlers17">Ehlers17</a>]</td></tr>
<tr><td class="idx">25</td><td class="idx"><a href="#N25L130D15">(130, 15)</a> <a href="#N25L131D13">(131, 13)</a> </td><td class="idx">100…130</td><td class="idx">10…13</td><td class="idx">Depth ubound: <a href="https://github.com/bertdobbelaere/SorterHunter">SorterHunter</a>. Size ubound: <a href="https://github.com/bertdobbelaere/SorterHunter">SorterHunter</a></td></tr>
<tr><td class="idx">26</td><td class="idx"><a href="#N26L139D14">(139, 14)</a> <a href="#N26L141D13">(141, 13)</a> </td><td class="idx">105…139</td><td class="idx">10…13</td><td class="idx">Depth ubound: <a href="https://github.com/bertdobbelaere/SorterHunter">SorterHunter</a>. Size ubound: <a href="https://github.com/bertdobbelaere/SorterHunter">SorterHunter</a></td></tr>
<tr><td class="idx">27</td><td class="idx"><a href="#N27L147D16">(147, 16)</a> <a href="#N27L148D14">(148, 14)</a> </td><td class="idx">110…147</td><td class="idx">10…14</td><td class="idx">Depth ubound: odd-even merge. Size ubound: <a href="https://github.com/bertdobbelaere/SorterHunter">SorterHunter</a></td></tr>
<tr><td class="idx">28</td><td class="idx"><a href="#N28L155D14">(155, 14)</a> </td><td class="idx">115…155</td><td class="idx">10…14</td><td class="idx">Depth ubound: odd-even merge. Size ubound: <a href="https://github.com/bertdobbelaere/SorterHunter">SorterHunter</a></td></tr>
<tr><td class="idx">29</td><td class="idx"><a href="#N29L164D15">(164, 15)</a> <a href="#N29L166D14">(166, 14)</a> </td><td class="idx">120…164</td><td class="idx">10…14</td><td class="idx">Depth ubound: odd-even merge. Size ubound: <a href="https://github.com/bertdobbelaere/SorterHunter">SorterHunter</a></td></tr>
<tr><td class="idx">30</td><td class="idx"><a href="#N30L172D14">(172, 14)</a> </td><td class="idx">125…172</td><td class="idx">10…14</td><td class="idx">Size/depth ubounds: <a href="https://en.wikipedia.org/wiki/Batcher_odd%E2%80%93even_mergesort">Batcher odd-even merge</a></td></tr>
<tr><td class="idx">31</td><td class="idx"><a href="#N31L180D14">(180, 14)</a> </td><td class="idx">130…180</td><td class="idx">10…14</td><td class="idx">Size/depth ubounds: <a href="https://en.wikipedia.org/wiki/Batcher_odd%E2%80%93even_mergesort">Batcher odd-even merge</a></td></tr>
<tr><td class="idx">32</td><td class="idx"><a href="#N32L185D14">(185, 14)</a> </td><td class="idx">135…185</td><td class="idx">10…14</td><td class="idx">Size/depth ubounds: <a href="https://en.wikipedia.org/wiki/Batcher_odd%E2%80%93even_mergesort">Batcher odd-even merge</a></td></tr>
<tr><td class="idx">33</td><td class="idx"><a href="#N33L199D16">(199, 16)</a> <a href="#N33L200D15">(200, 15)</a> </td><td class="idx">141…199</td><td class="idx">10…15</td><td class="idx">Size ubound: <a href="https://github.com/bertdobbelaere/SorterHunter">SorterHunter</a>, depth ubound: <a href="https://en.wikipedia.org/wiki/Batcher_odd%E2%80%93even_mergesort">Batcher odd-even merge</a></td></tr>
<tr><td class="idx">34</td><td class="idx"><a href="#N34L209D17">(209, 17)</a> <a href="#N34L210D16">(210, 16)</a> <a href="#N34L213D15">(213, 15)</a> </td><td class="idx">147…209</td><td class="idx">10…15</td><td class="idx">Size and depth ubound: <a href="https://github.com/bertdobbelaere/SorterHunter">SorterHunter</a></td></tr>
<tr><td class="idx">35</td><td class="idx"><a href="#N35L220D17">(220, 17)</a> <a href="#N35L221D16">(221, 16)</a> </td><td class="idx">153…220</td><td class="idx">10…16</td><td class="idx">Size ubound: <a href="https://github.com/bertdobbelaere/SorterHunter">SorterHunter</a>, depth ubound: <a href="https://en.wikipedia.org/wiki/Batcher_odd%E2%80%93even_mergesort">Batcher odd-even merge</a></td></tr>
<tr><td class="idx">36</td><td class="idx"><a href="#N36L227D18">(227, 18)</a> <a href="#N36L228D17">(228, 17)</a> <a href="#N36L229D16">(229, 16)</a> </td><td class="idx">159…227</td><td class="idx">10…16</td><td class="idx">Size ubound: <a href="https://github.com/bertdobbelaere/SorterHunter">SorterHunter</a>, depth ubound: <a href="https://en.wikipedia.org/wiki/Batcher_odd%E2%80%93even_mergesort">Batcher odd-even merge</a></td></tr>
<tr><td class="idx">37</td><td class="idx"><a href="#N37L240D17">(240, 17)</a> <a href="#N37L243D16">(243, 16)</a> </td><td class="idx">165…240</td><td class="idx">10…16</td><td class="idx">Size ubound: <a href="https://github.com/bertdobbelaere/SorterHunter">SorterHunter</a>, depth ubound: Van Voorhis (4,4) merge.</td></tr>
<tr><td class="idx">38</td><td class="idx"><a href="#N38L250D17">(250, 17)</a> <a href="#N38L255D16">(255, 16)</a> </td><td class="idx">171…250</td><td class="idx">10…16</td><td class="idx">Size ubound: <a href="https://github.com/bertdobbelaere/SorterHunter">SorterHunter</a>, depth ubound: Van Voorhis (4,4) merge.</td></tr>
<tr><td class="idx">39</td><td class="idx"><a href="#N39L259D17">(259, 17)</a> <a href="#N39L263D16">(263, 16)</a> </td><td class="idx">177…259</td><td class="idx">10…16</td><td class="idx">Size ubound: <a href="https://github.com/bertdobbelaere/SorterHunter">SorterHunter</a>, depth ubound: Van Voorhis (4,4) merge.</td></tr>
<tr><td class="idx">40</td><td class="idx"><a href="#N40L265D17">(265, 17)</a> <a href="#N40L269D16">(269, 16)</a> </td><td class="idx">183…265</td><td class="idx">10…16</td><td class="idx">Size ubound: <a href="https://github.com/bertdobbelaere/SorterHunter">SorterHunter</a>, depth ubound: Van Voorhis (4,4) merge.</td></tr>
<tr><td class="idx">41</td><td class="idx"><a href="#N41L282D19">(282, 19)</a> <a href="#N41L283D18">(283, 18)</a> <a href="#N41L288D17">(288, 17)</a> </td><td class="idx">189…282</td><td class="idx">10…17</td><td class="idx">Size ubound: <a href="https://github.com/bertdobbelaere/SorterHunter">SorterHunter</a>, depth ubound: Van Voorhis (4,4) merge.</td></tr>
<tr><td class="idx">42</td><td class="idx"><a href="#N42L291D18">(291, 18)</a> <a href="#N42L294D17">(294, 17)</a> </td><td class="idx">195…291</td><td class="idx">10…17</td><td class="idx">Size and depth ubound: <a href="https://github.com/bertdobbelaere/SorterHunter">SorterHunter</a></td></tr>
<tr><td class="idx">43</td><td class="idx"><a href="#N43L303D19">(303, 19)</a> <a href="#N43L305D17">(305, 17)</a> </td><td class="idx">201…303</td><td class="idx">10…17</td><td class="idx">Size and depth ubound: <a href="https://github.com/bertdobbelaere/SorterHunter">SorterHunter</a></td></tr>
<tr><td class="idx">44</td><td class="idx"><a href="#N44L309D19">(309, 19)</a> <a href="#N44L311D17">(311, 17)</a> </td><td class="idx">207…309</td><td class="idx">10…17</td><td class="idx">Size and depth ubound: <a href="https://github.com/bertdobbelaere/SorterHunter">SorterHunter</a></td></tr>
<tr><td class="idx">45</td><td class="idx"><a href="#N45L324D19">(324, 19)</a> <a href="#N45L325D18">(325, 18)</a> </td><td class="idx">213…324</td><td class="idx">10…18</td><td class="idx">Size ubound: <a href="https://github.com/bertdobbelaere/SorterHunter">SorterHunter</a>, depth ubound: Van Voorhis (4,4) merge.</td></tr>
<tr><td class="idx">46</td><td class="idx"><a href="#N46L332D19">(332, 19)</a> <a href="#N46L333D18">(333, 18)</a> </td><td class="idx">219…332</td><td class="idx">10…18</td><td class="idx">Size ubound: <a href="https://github.com/bertdobbelaere/SorterHunter">SorterHunter</a>, depth ubound: <a href="https://en.wikipedia.org/wiki/Batcher_odd%E2%80%93even_mergesort">Batcher odd-even merge</a>.</td></tr>
<tr><td class="idx">47</td><td class="idx"><a href="#N47L340D19">(340, 19)</a> <a href="#N47L341D18">(341, 18)</a> </td><td class="idx">225…340</td><td class="idx">10…18</td><td class="idx">Size ubound: <a href="https://github.com/bertdobbelaere/SorterHunter">SorterHunter</a>, depth ubound: <a href="https://en.wikipedia.org/wiki/Batcher_odd%E2%80%93even_mergesort">Batcher odd-even merge</a>.</td></tr>
<tr><td class="idx">48</td><td class="idx"><a href="#N48L346D19">(346, 19)</a> <a href="#N48L347D18">(347, 18)</a> </td><td class="idx">231…346</td><td class="idx">10…18</td><td class="idx">Size ubound: <a href="https://github.com/bertdobbelaere/SorterHunter">SorterHunter</a>, depth ubound: <a href="https://en.wikipedia.org/wiki/Batcher_odd%E2%80%93even_mergesort">Batcher odd-even merge</a>.</td></tr>
<tr><td class="idx">49</td><td class="idx"><a href="#N49L365D21">(365, 21)</a> <a href="#N49L370D20">(370, 20)</a> <a href="#N49L371D19">(371, 19)</a> </td><td class="idx">237…365</td><td class="idx">10…19</td><td class="idx">Size ubound: Van Voorhis (4,4) merge, depth ubound: <a href="https://en.wikipedia.org/wiki/Batcher_odd%E2%80%93even_mergesort">Batcher odd-even merge</a>.</td></tr>
<tr><td class="idx">50</td><td class="idx"><a href="#N50L376D21">(376, 21)</a> <a href="#N50L379D20">(379, 20)</a> <a href="#N50L381D19">(381, 19)</a> </td><td class="idx">243…376</td><td class="idx">10…19</td><td class="idx">Size ubound: Van Voorhis (4,4) merge, depth ubound: <a href="https://en.wikipedia.org/wiki/Batcher_odd%E2%80%93even_mergesort">Batcher odd-even merge</a>.</td></tr>
<tr><td class="idx">51</td><td class="idx"><a href="#N51L387D22">(387, 22)</a> <a href="#N51L389D20">(389, 20)</a> <a href="#N51L396D19">(396, 19)</a> </td><td class="idx">249…387</td><td class="idx">10…19</td><td class="idx">Size ubound: Van Voorhis (4,4) merge, depth ubound: <a href="https://en.wikipedia.org/wiki/Batcher_odd%E2%80%93even_mergesort">Batcher odd-even merge</a>.</td></tr>
<tr><td class="idx">52</td><td class="idx"><a href="#N52L395D20">(395, 20)</a> <a href="#N52L407D19">(407, 19)</a> </td><td class="idx">255…395</td><td class="idx">10…19</td><td class="idx">Size ubound: Van Voorhis (4,4) merge, depth ubound: <a href="https://en.wikipedia.org/wiki/Batcher_odd%E2%80%93even_mergesort">Batcher odd-even merge</a>.</td></tr>
<tr><td class="idx">53</td><td class="idx"><a href="#N53L411D22">(411, 22)</a> <a href="#N53L412D21">(412, 21)</a> <a href="#N53L415D20">(415, 20)</a> </td><td class="idx">261…411</td><td class="idx">11…20</td><td class="idx">Size/depth ubound: Van Voorhis (4,4) merge. Depth lbound: max 26 pairs per layer, size lbound wouldn't fit in 10 layers.</td></tr>
<tr><td class="idx">54</td><td class="idx"><a href="#N54L421D20">(421, 20)</a> </td><td class="idx">267…421</td><td class="idx">11…20</td><td class="idx">Size ubound: <a href="https://github.com/bertdobbelaere/SorterHunter">SorterHunter</a>, depth ubound: <a href="https://en.wikipedia.org/wiki/Batcher_odd%E2%80%93even_mergesort">Batcher odd-even merge</a>.</td></tr>
<tr><td class="idx">55</td><td class="idx"><a href="#N55L432D20">(432, 20)</a> </td><td class="idx">273…432</td><td class="idx">11…20</td><td class="idx">Size ubound: <a href="https://github.com/bertdobbelaere/SorterHunter">SorterHunter</a>, depth ubound: <a href="https://en.wikipedia.org/wiki/Batcher_odd%E2%80%93even_mergesort">Batcher odd-even merge</a>.</td></tr>
<tr><td class="idx">56</td><td class="idx"><a href="#N56L438D20">(438, 20)</a> </td><td class="idx">279…438</td><td class="idx">11…20</td><td class="idx">Size ubound: <a href="https://github.com/bertdobbelaere/SorterHunter">SorterHunter</a>, depth ubound: Van Voorhis (4,4) merge.</td></tr>
<tr><td class="idx">57</td><td class="idx"><a href="#N57L454D21">(454, 21)</a> <a href="#N57L461D20">(461, 20)</a> </td><td class="idx">285…454</td><td class="idx">11…20</td><td class="idx">Size ubound: Van Voorhis (4,4) merge, depth ubound: <a href="https://en.wikipedia.org/wiki/Batcher_odd%E2%80%93even_mergesort">Batcher odd-even merge</a></td></tr>
<tr><td class="idx">58</td><td class="idx"><a href="#N58L465D21">(465, 21)</a> <a href="#N58L471D20">(471, 20)</a> </td><td class="idx">291…465</td><td class="idx">11…20</td><td class="idx">Size ubound: Van Voorhis (4,4) merge, depth ubound: <a href="https://en.wikipedia.org/wiki/Batcher_odd%E2%80%93even_mergesort">Batcher odd-even merge</a></td></tr>
<tr><td class="idx">59</td><td class="idx"><a href="#N59L476D21">(476, 21)</a> <a href="#N59L480D20">(480, 20)</a> </td><td class="idx">297…476</td><td class="idx">11…20</td><td class="idx">Size ubound: Van Voorhis (4,4) merge, depth ubound: <a href="https://en.wikipedia.org/wiki/Batcher_odd%E2%80%93even_mergesort">Batcher odd-even merge</a></td></tr>
<tr><td class="idx">60</td><td class="idx"><a href="#N60L483D21">(483, 21)</a> <a href="#N60L489D20">(489, 20)</a> </td><td class="idx">303…483</td><td class="idx">11…20</td><td class="idx">Size ubound: Van Voorhis (4,4) merge, depth ubound: <a href="https://en.wikipedia.org/wiki/Batcher_odd%E2%80%93even_mergesort">Batcher odd-even merge</a></td></tr>
<tr><td class="idx">61</td><td class="idx"><a href="#N61L497D22">(497, 22)</a> <a href="#N61L498D21">(498, 21)</a> <a href="#N61L502D20">(502, 20)</a> </td><td class="idx">309…497</td><td class="idx">11…20</td><td class="idx">Size ubound: Van Voorhis (4,4) merge, depth ubound: <a href="https://en.wikipedia.org/wiki/Batcher_odd%E2%80%93even_mergesort">Batcher odd-even merge</a></td></tr>
<tr><td class="idx">62</td><td class="idx"><a href="#N62L506D21">(506, 21)</a> <a href="#N62L511D20">(511, 20)</a> </td><td class="idx">315…506</td><td class="idx">11…20</td><td class="idx">Size ubound: Van Voorhis (4,4) merge, depth ubound: <a href="https://en.wikipedia.org/wiki/Batcher_odd%E2%80%93even_mergesort">Batcher odd-even merge</a></td></tr>
<tr><td class="idx">63</td><td class="idx"><a href="#N63L515D21">(515, 21)</a> <a href="#N63L519D20">(519, 20)</a> </td><td class="idx">321…515</td><td class="idx">11…20</td><td class="idx">Size ubound: Van Voorhis (4,4) merge, depth ubound: <a href="https://en.wikipedia.org/wiki/Batcher_odd%E2%80%93even_mergesort">Batcher odd-even merge</a></td></tr>
<tr><td class="idx">64</td><td class="idx"><a href="#N64L521D21">(521, 21)</a> <a href="#N64L525D20">(525, 20)</a> </td><td class="idx">327…521</td><td class="idx">11…20</td><td class="idx">Size ubound: [<a href="#VVoorh71b">VVoorh71b</a>]. See same reference for input counts of larger powers of 2. Depth ubound: <a href="https://en.wikipedia.org/wiki/Batcher_odd%E2%80%93even_mergesort">Batcher odd-even merge</a></td></tr>
</table>
<h3>Individual networks:</h3>
<table id=Networks>
<tr id="N2L1D1"><td>Sorting network for 2 inputs, 1 CE, 1 layer:<br>
<p class="mono">[(0,1)]<br>
</p>Trivial sorting network for two inputs. The only simpler "network" is the one for one input, which uses no CE at all and is represented by a horizontal line.</td><td>
Auto generated</td></tr>
<tr id="N3L3D3"><td>Sorting network for 3 inputs, 3 CEs, 3 layers:<br>
<p class="mono">[(0,2)]<br>
[(0,1)]<br>
[(1,2)]<br>
</p></td><td>
Auto generated</td></tr>
<tr id="N4L5D3"><td>Sorting network for 4 inputs, 5 CEs, 3 layers:<br>
<p class="mono">[(0,2),(1,3)]<br>
[(0,1),(2,3)]<br>
[(1,2)]<br>
</p></td><td>
Auto generated</td></tr>
<tr id="N5L9D5"><td>Sorting network for 5 inputs, 9 CEs, 5 layers:<br>
<p class="mono">[(0,3),(1,4)]<br>
[(0,2),(1,3)]<br>
[(0,1),(2,4)]<br>
[(1,2),(3,4)]<br>
[(2,3)]<br>
</p></td><td>
Auto generated</td></tr>
<tr id="N6L12D5"><td>Sorting network for 6 inputs, 12 CEs, 5 layers:<br>
<p class="mono">[(0,5),(1,3),(2,4)]<br>
[(1,2),(3,4)]<br>
[(0,3),(2,5)]<br>
[(0,1),(2,3),(4,5)]<br>
[(1,2),(3,4)]<br>
</p></td><td>
Auto generated</td></tr>
<tr id="N7L16D6"><td>Sorting network for 7 inputs, 16 CEs, 6 layers:<br>
<p class="mono">[(0,6),(2,3),(4,5)]<br>
[(0,2),(1,4),(3,6)]<br>
[(0,1),(2,5),(3,4)]<br>
[(1,2),(4,6)]<br>
[(2,3),(4,5)]<br>
[(1,2),(3,4),(5,6)]<br>
</p></td><td>
Auto generated</td></tr>
<tr id="N8L19D6"><td>Sorting network for 8 inputs, 19 CEs, 6 layers:<br>
<p class="mono">[(0,2),(1,3),(4,6),(5,7)]<br>
[(0,4),(1,5),(2,6),(3,7)]<br>
[(0,1),(2,3),(4,5),(6,7)]<br>
[(2,4),(3,5)]<br>
[(1,4),(3,6)]<br>
[(1,2),(3,4),(5,6)]<br>
</p></td><td>
Auto generated</td></tr>
<tr id="N9L25D7"><td>Sorting network for 9 inputs, 25 CEs, 7 layers:<br>
<p class="mono">[(0,3),(1,7),(2,5),(4,8)]<br>
[(0,7),(2,4),(3,8),(5,6)]<br>
[(0,2),(1,3),(4,5),(7,8)]<br>
[(1,4),(3,6),(5,7)]<br>
[(0,1),(2,4),(3,5),(6,8)]<br>
[(2,3),(4,5),(6,7)]<br>
[(1,2),(3,4),(5,6)]<br>
</p></td><td>
Auto generated</td></tr>
<tr id="N10L29D8"><td>Sorting network for 10 inputs, 29 CEs, 8 layers:<br>
<p class="mono">[(0,8),(1,9),(2,7),(3,5),(4,6)]<br>
[(0,2),(1,4),(5,8),(7,9)]<br>
[(0,3),(2,4),(5,7),(6,9)]<br>
[(0,1),(3,6),(8,9)]<br>
[(1,5),(2,3),(4,8),(6,7)]<br>
[(1,2),(3,5),(4,6),(7,8)]<br>
[(2,3),(4,5),(6,7)]<br>
[(3,4),(5,6)]<br>
</p></td><td>
Auto generated</td></tr>
<tr id="N10L31D7"><td>Sorting network for 10 inputs, 31 CEs, 7 layers:<br>
<p class="mono">[(0,1),(2,5),(3,6),(4,7),(8,9)]<br>
[(0,6),(1,8),(2,4),(3,9),(5,7)]<br>
[(0,2),(1,3),(4,5),(6,8),(7,9)]<br>
[(0,1),(2,7),(3,5),(4,6),(8,9)]<br>
[(1,2),(3,4),(5,6),(7,8)]<br>
[(1,3),(2,4),(5,7),(6,8)]<br>
[(2,3),(4,5),(6,7)]<br>
</p>31 is the optimal size for 7 layers [<a href="#Fon18">Fon18</a>]</td><td>
Auto generated</td></tr>
<tr id="N11L35D8"><td>Sorting network for 11 inputs, 35 CEs, 8 layers:<br>
<p class="mono">[(0,9),(1,6),(2,4),(3,7),(5,8)]<br>
[(0,1),(3,5),(4,10),(6,9),(7,8)]<br>
[(1,3),(2,5),(4,7),(8,10)]<br>
[(0,4),(1,2),(3,7),(5,9),(6,8)]<br>
[(0,1),(2,6),(4,5),(7,8),(9,10)]<br>
[(2,4),(3,6),(5,7),(8,9)]<br>
[(1,2),(3,4),(5,6),(7,8)]<br>
[(2,3),(4,5),(6,7)]<br>
</p>35 is the optimal size [<a href="#Harder19">Harder19</a>] (see also [<a href="#Fon18">Fon18</a>] for 8 or 9 layers).</td><td>
Auto generated</td></tr>
<tr id="N12L39D9"><td>Sorting network for 12 inputs, 39 CEs, 9 layers:<br>
<p class="mono">[(0,8),(1,7),(2,6),(3,11),(4,10),(5,9)]<br>
[(0,1),(2,5),(3,4),(6,9),(7,8),(10,11)]<br>
[(0,2),(1,6),(5,10),(9,11)]<br>
[(0,3),(1,2),(4,6),(5,7),(8,11),(9,10)]<br>
[(1,4),(3,5),(6,8),(7,10)]<br>
[(1,3),(2,5),(6,9),(8,10)]<br>
[(2,3),(4,5),(6,7),(8,9)]<br>
[(4,6),(5,7)]<br>
[(3,4),(5,6),(7,8)]<br>
</p>39 is the optimal size [<a href="#Harder19">Harder19</a>] (see also [<a href="#Fon18">Fon18</a>] for 9 layers).</td><td>
Auto generated</td></tr>
<tr id="N12L40D8"><td>Sorting network for 12 inputs, 40 CEs, 8 layers:<br>
<p class="mono">[(0,8),(1,7),(2,6),(3,11),(4,10),(5,9)]<br>
[(0,2),(1,4),(3,5),(6,8),(7,10),(9,11)]<br>
[(0,1),(2,9),(4,7),(5,6),(10,11)]<br>
[(1,3),(2,7),(4,9),(8,10)]<br>
[(0,1),(2,3),(4,5),(6,7),(8,9),(10,11)]<br>
[(1,2),(3,5),(6,8),(9,10)]<br>
[(2,4),(3,6),(5,8),(7,9)]<br>
[(1,2),(3,4),(5,6),(7,8),(9,10)]<br>
</p>40 is the optimal size for 8 layers [<a href="#Fon18">Fon18</a>].</td><td>
Auto generated</td></tr>
<tr id="N13L45D10"><td>Sorting network for 13 inputs, 45 CEs, 10 layers:<br>
<p class="mono">[(0,12),(1,10),(2,9),(3,7),(5,11),(6,8)]<br>
[(1,6),(2,3),(4,11),(7,9),(8,10)]<br>
[(0,4),(1,2),(3,6),(7,8),(9,10),(11,12)]<br>
[(4,6),(5,9),(8,11),(10,12)]<br>
[(0,5),(3,8),(4,7),(6,11),(9,10)]<br>
[(0,1),(2,5),(6,9),(7,8),(10,11)]<br>
[(1,3),(2,4),(5,6),(9,10)]<br>
[(1,2),(3,4),(5,7),(6,8)]<br>
[(2,3),(4,5),(6,7),(8,9)]<br>
[(3,4),(5,6)]<br>
</p></td><td>
Auto generated</td></tr>
<tr id="N13L46D9"><td>Sorting network for 13 inputs, 46 CEs, 9 layers:<br>
<p class="mono">[(0,11),(1,7),(2,4),(3,5),(8,9),(10,12)]<br>
[(0,2),(3,6),(4,12),(5,7),(8,10)]<br>
[(0,8),(1,3),(2,5),(4,9),(6,11),(7,12)]<br>
[(0,1),(2,10),(3,8),(4,6),(9,11)]<br>
[(1,3),(2,4),(5,10),(6,8),(7,9),(11,12)]<br>
[(1,2),(3,4),(5,8),(6,9),(7,10)]<br>
[(2,3),(4,7),(5,6),(8,11),(9,10)]<br>
[(4,5),(6,7),(8,9),(10,11)]<br>
[(3,4),(5,6),(7,8),(9,10)]<br>
</p></td><td>
Auto generated</td></tr>
<tr id="N14L51D10"><td>Sorting network for 14 inputs, 51 CEs, 10 layers:<br>
<p class="mono">[(0,1),(2,3),(4,5),(6,7),(8,9),(10,11),(12,13)]<br>
[(0,2),(1,3),(4,8),(5,9),(10,12),(11,13)]<br>
[(0,4),(1,2),(3,7),(5,8),(6,10),(9,13),(11,12)]<br>
[(0,6),(1,5),(3,9),(4,10),(7,13),(8,12)]<br>
[(2,10),(3,11),(4,6),(7,9)]<br>
[(1,3),(2,8),(5,11),(6,7),(10,12)]<br>
[(1,4),(2,6),(3,5),(7,11),(8,10),(9,12)]<br>
[(2,4),(3,6),(5,8),(7,10),(9,11)]<br>
[(3,4),(5,6),(7,8),(9,10)]<br>
[(6,7)]<br>
</p>Front-concentrated, only single element in last layer</td><td>
Auto generated</td></tr>
<tr id="N14L52D9"><td>Sorting network for 14 inputs, 52 CEs, 9 layers:<br>
<p class="mono">[(0,1),(2,3),(4,5),(6,7),(8,9),(10,11),(12,13)]<br>
[(0,2),(1,3),(4,8),(5,9),(10,12),(11,13)]<br>
[(0,10),(1,6),(2,11),(3,13),(5,8),(7,12)]<br>
[(1,4),(2,8),(3,6),(5,11),(7,10),(9,12)]<br>
[(0,1),(3,9),(4,10),(5,7),(6,8),(12,13)]<br>
[(1,5),(2,4),(3,7),(6,10),(8,12),(9,11)]<br>
[(1,2),(3,5),(4,6),(7,9),(8,10),(11,12)]<br>
[(2,3),(4,5),(6,7),(8,9),(10,11)]<br>
[(3,4),(5,6),(7,8),(9,10)]<br>
</p>Symmetric variant replacing asymmetric predecessor, was surprisingly hard to find using <a href="https://github.com/bertdobbelaere/SorterHunter">SorterHunter</a>.</td><td>
Auto generated</td></tr>
<tr id="N15L56D10"><td>Sorting network for 15 inputs, 56 CEs, 10 layers:<br>
<p class="mono">[(1,2),(3,10),(4,14),(5,8),(6,13),(7,12),(9,11)]<br>
[(0,14),(1,5),(2,8),(3,7),(6,9),(10,12),(11,13)]<br>
[(0,7),(1,6),(2,9),(4,10),(5,11),(8,13),(12,14)]<br>
[(0,6),(2,4),(3,5),(7,11),(8,10),(9,12),(13,14)]<br>
[(0,3),(1,2),(4,7),(5,9),(6,8),(10,11),(12,13)]<br>
[(0,1),(2,3),(4,6),(7,9),(10,12),(11,13)]<br>
[(1,2),(3,5),(8,10),(11,12)]<br>
[(3,4),(5,6),(7,8),(9,10)]<br>
[(2,3),(4,5),(6,7),(8,9),(10,11)]<br>
[(5,6),(7,8)]<br>
</p></td><td>
Auto generated</td></tr>
<tr id="N15L57D9"><td>Sorting network for 15 inputs, 57 CEs, 9 layers:<br>
<p class="mono">[(0,6),(1,10),(2,14),(3,9),(4,12),(5,13),(7,11)]<br>
[(0,7),(2,5),(3,4),(6,11),(8,10),(9,12),(13,14)]<br>
[(1,13),(2,3),(4,6),(5,9),(7,8),(10,14),(11,12)]<br>
[(0,3),(1,4),(5,7),(6,13),(8,9),(10,11),(12,14)]<br>
[(0,2),(1,5),(3,8),(4,6),(7,10),(9,11),(12,13)]<br>
[(0,1),(2,5),(3,10),(4,8),(6,7),(9,12),(11,13)]<br>
[(1,2),(3,4),(5,6),(7,9),(8,10),(11,12)]<br>
[(3,5),(4,6),(7,8),(9,10)]<br>
[(2,3),(4,5),(6,7),(8,9),(10,11)]<br>
</p></td><td>
Auto generated</td></tr>
<tr id="N16L60D10"><td>Sorting network for 16 inputs, 60 CEs, 10 layers:<br>
<p class="mono">[(0,13),(1,12),(2,15),(3,14),(4,8),(5,6),(7,11),(9,10)]<br>
[(0,5),(1,7),(2,9),(3,4),(6,13),(8,14),(10,15),(11,12)]<br>
[(0,1),(2,3),(4,5),(6,8),(7,9),(10,11),(12,13),(14,15)]<br>
[(0,2),(1,3),(4,10),(5,11),(6,7),(8,9),(12,14),(13,15)]<br>
[(1,2),(3,12),(4,6),(5,7),(8,10),(9,11),(13,14)]<br>
[(1,4),(2,6),(5,8),(7,10),(9,13),(11,14)]<br>
[(2,4),(3,6),(9,12),(11,13)]<br>
[(3,5),(6,8),(7,9),(10,12)]<br>
[(3,4),(5,6),(7,8),(9,10),(11,12)]<br>
[(6,7),(8,9)]<br>
</p>Size and depth match the handcrafted network of M.W. Green, 1969 [<a href="#TAOCPv3">TAOCPv3</a>]. It is remarkable that the last three layers (found by independent computer search) are identical to those in Green's network.</td><td>
Auto generated</td></tr>
<tr id="N16L61D9"><td>Sorting network for 16 inputs, 61 CEs, 9 layers:<br>
<p class="mono">[(0,5),(1,4),(2,12),(3,13),(6,7),(8,9),(10,15),(11,14)]<br>
[(0,2),(1,10),(3,6),(4,7),(5,14),(8,11),(9,12),(13,15)]<br>
[(0,8),(1,3),(2,11),(4,13),(5,9),(6,10),(7,15),(12,14)]<br>
[(0,1),(2,4),(3,8),(5,6),(7,12),(9,10),(11,13),(14,15)]<br>
[(1,3),(2,5),(4,8),(6,9),(7,11),(10,13),(12,14)]<br>
[(1,2),(3,5),(4,11),(6,8),(7,9),(10,12),(13,14)]<br>
[(2,3),(4,5),(6,7),(8,9),(10,11),(12,13)]<br>
[(4,6),(5,7),(8,10),(9,11)]<br>
[(3,4),(5,6),(7,8),(9,10),(11,12)]<br>
</p></td><td>
Auto generated</td></tr>
<tr id="N17L71D12"><td>Sorting network for 17 inputs, 71 CEs, 12 layers:<br>
<p class="mono">[(0,11),(1,15),(2,10),(3,5),(4,6),(8,12),(9,16),(13,14)]<br>
[(0,6),(1,13),(2,8),(4,14),(5,15),(7,11)]<br>
[(0,8),(3,7),(4,9),(6,16),(10,11),(12,14)]<br>
[(0,2),(1,4),(5,6),(7,13),(8,9),(10,12),(11,14),(15,16)]<br>
[(0,3),(2,5),(6,11),(7,10),(9,13),(12,15),(14,16)]<br>
[(0,1),(3,4),(5,10),(6,9),(7,8),(11,15),(13,14)]<br>
[(1,2),(3,7),(4,8),(6,12),(11,13),(14,15)]<br>
[(1,3),(2,7),(4,5),(9,11),(10,12),(13,14)]<br>
[(2,3),(4,6),(5,7),(8,10)]<br>
[(3,4),(6,8),(7,9),(10,12)]<br>
[(5,6),(7,8),(9,10),(11,12)]<br>
[(4,5),(6,7),(8,9),(10,11),(12,13)]<br>
</p>Size matches result from Valsalam & Miikkulainen [<a href="#VM13">VM13</a>]. Depth reduced from 17 to 12.</td><td>
Auto generated</td></tr>
<tr id="N17L72D11"><td>Sorting network for 17 inputs, 72 CEs, 11 layers:<br>
<p class="mono">[(0,8),(1,3),(2,6),(4,15),(5,13),(9,16),(10,11),(12,14)]<br>
[(0,2),(1,4),(3,15),(5,8),(6,14),(7,9),(13,16)]<br>
[(2,13),(3,11),(5,10),(6,9),(7,12),(8,15),(14,16)]<br>
[(0,7),(1,5),(3,6),(4,10),(8,14),(9,11),(12,13),(15,16)]<br>
[(0,1),(2,6),(4,12),(5,7),(9,14),(10,13),(11,15)]<br>
[(1,4),(2,3),(6,11),(7,12),(8,9),(13,14),(15,16)]<br>
[(2,5),(3,8),(7,10),(9,12),(11,13),(14,15)]<br>
[(1,2),(3,7),(4,5),(6,9),(8,10),(13,14)]<br>
[(3,4),(5,7),(6,8),(9,11),(10,12)]<br>
[(2,4),(5,6),(7,8),(9,10),(11,12)]<br>
[(2,3),(4,5),(6,7),(8,9),(10,11),(12,13)]<br>
</p></td><td>
Auto generated</td></tr>
<tr id="N17L74D10"><td>Sorting network for 17 inputs, 74 CEs, 10 layers:<br>
<p class="mono">[(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16)]<br>
[(1,3),(2,4),(5,7),(6,8),(9,11),(10,12),(13,15),(14,16)]<br>
[(1,5),(2,6),(3,7),(4,8),(9,13),(10,14),(11,15),(12,16)]<br>
[(0,3),(1,13),(2,10),(4,7),(5,11),(6,12),(8,9),(14,15)]<br>
[(0,13),(1,8),(2,5),(3,6),(4,14),(7,15),(9,16),(10,11)]<br>
[(0,1),(2,8),(3,4),(5,10),(6,13),(7,11),(12,14)]<br>
[(1,5),(3,8),(4,10),(6,7),(9,12),(11,13)]<br>
[(1,2),(4,6),(5,8),(7,10),(9,11),(12,14),(13,15)]<br>
[(2,3),(4,5),(6,8),(7,9),(10,11),(12,13),(14,15)]<br>
[(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16)]<br>
</p>This network was obtained by performing a size optimization of the network found by Ehlers&Müller (see [<a href="#EM14">EM14</a>])</td><td>
Auto generated</td></tr>
<tr id="N18L77D12"><td>Sorting network for 18 inputs, 77 CEs, 12 layers:<br>
<p class="mono">[(0,1),(2,3),(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17)]<br>
[(0,2),(1,3),(4,12),(5,13),(6,8),(9,11),(14,16),(15,17)]<br>
[(0,14),(1,16),(2,15),(3,17)]<br>
[(0,6),(1,10),(2,9),(7,16),(8,15),(11,17)]<br>
[(1,4),(3,9),(5,7),(8,14),(10,12),(13,16)]<br>
[(0,1),(2,5),(3,13),(4,14),(7,9),(8,10),(12,15),(16,17)]<br>
[(1,2),(3,5),(4,6),(11,13),(12,14),(15,16)]<br>
[(4,8),(5,12),(6,10),(7,11),(9,13)]<br>
[(1,4),(2,8),(3,6),(5,7),(9,15),(10,12),(11,14),(13,16)]<br>
[(2,4),(5,8),(6,10),(7,11),(9,12),(13,15)]<br>
[(3,5),(6,8),(7,10),(9,11),(12,14)]<br>
[(3,4),(5,6),(7,8),(9,10),(11,12),(13,14)]<br>
</p>Improved size over result (78) reported in [<a href="#VM13">VM13</a>].</td><td>
Auto generated</td></tr>
<tr id="N18L78D11"><td>Sorting network for 18 inputs, 78 CEs, 11 layers:<br>
<p class="mono">[(0,6),(1,10),(2,15),(3,5),(4,9),(7,16),(8,13),(11,17),(12,14)]<br>
[(0,12),(1,4),(3,11),(5,17),(6,14),(7,8),(9,10),(13,16)]<br>
[(1,13),(2,7),(4,16),(6,9),(8,11),(10,15)]<br>
[(0,1),(2,3),(4,12),(5,13),(7,9),(8,10),(14,15),(16,17)]<br>
[(0,2),(1,11),(3,4),(5,7),(6,16),(10,12),(13,14),(15,17)]<br>
[(1,8),(4,10),(5,6),(7,13),(9,16),(11,12)]<br>
[(1,3),(2,5),(4,7),(6,8),(9,11),(10,13),(12,15),(14,16)]<br>
[(1,2),(3,5),(4,6),(7,9),(8,10),(11,13),(12,14),(15,16)]<br>
[(2,3),(5,8),(6,7),(9,12),(10,11),(14,15)]<br>
[(3,4),(5,6),(7,8),(9,10),(11,12),(13,14)]<br>
[(4,5),(6,7),(8,9),(10,11),(12,13)]<br>
</p>Matches depth of 11 layers reported in [<a href="#Baddar09">Baddar09</a>] while reducing size from 84 to 78.</td><td>
Auto generated</td></tr>
<tr id="N19L85D12"><td>Sorting network for 19 inputs, 85 CEs, 12 layers:<br>
<p class="mono">[(0,12),(1,4),(2,8),(3,5),(6,17),(7,11),(9,14),(10,13),(15,16)]<br>
[(0,2),(1,7),(3,6),(4,11),(5,17),(8,12),(10,15),(13,16),(14,18)]<br>
[(3,10),(4,14),(5,15),(6,13),(7,9),(11,17),(16,18)]<br>
[(0,7),(1,10),(4,6),(9,15),(11,16),(12,17),(13,14)]<br>
[(0,3),(2,6),(5,7),(8,11),(12,16)]<br>
[(1,8),(2,9),(3,4),(6,15),(7,13),(10,11),(12,18)]<br>
[(1,3),(2,5),(6,9),(7,12),(8,10),(11,14),(17,18)]<br>
[(0,1),(2,3),(4,8),(6,10),(9,12),(14,15),(16,17)]<br>
[(1,2),(5,8),(6,7),(9,11),(10,13),(14,16),(15,17)]<br>
[(3,6),(4,5),(7,9),(8,10),(11,12),(13,14),(15,16)]<br>
[(3,4),(5,6),(7,8),(9,10),(11,13),(12,14)]<br>
[(2,3),(4,5),(6,7),(8,9),(10,11),(12,13),(14,15)]<br>
</p>Improved size over result (86) reported by Valsalam & Miikkulainen [<a href="#VM13">VM13</a>]</td><td>
Auto generated</td></tr>
<tr id="N19L87D11"><td>Sorting network for 19 inputs, 87 CEs, 11 layers:<br>
<p class="mono">[(0,1),(2,3),(4,5),(6,7),(8,10),(11,12),(13,14),(15,16),(17,18)]<br>
[(0,2),(1,3),(4,6),(5,7),(8,9),(11,13),(12,14),(15,17),(16,18)]<br>
[(0,4),(1,5),(2,6),(3,7),(9,10),(11,15),(12,16),(13,17),(14,18)]<br>
[(0,11),(1,8),(2,13),(3,17),(4,10),(5,6),(9,16),(12,15)]<br>
[(1,2),(3,13),(4,12),(5,14),(6,16),(7,10),(8,15)]<br>
[(0,1),(2,11),(3,9),(5,12),(6,15),(7,13),(10,18),(14,17)]<br>
[(1,4),(3,8),(5,11),(6,9),(7,12),(10,13),(14,15),(16,17)]<br>
[(2,4),(3,5),(6,7),(8,11),(9,12),(10,14),(13,15)]<br>
[(2,3),(4,5),(6,8),(7,9),(10,11),(12,14),(13,16),(15,17)]<br>
[(1,2),(4,6),(5,8),(7,10),(9,11),(12,13),(14,16)]<br>
[(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16)]<br>
</p></td><td>
Auto generated</td></tr>
<tr id="N20L91D12"><td>Sorting network for 20 inputs, 91 CEs, 12 layers:<br>
<p class="mono">[(0,3),(1,7),(2,5),(4,8),(6,9),(10,13),(11,15),(12,18),(14,17),(16,19)]<br>
[(0,14),(1,11),(2,16),(3,17),(4,12),(5,19),(6,10),(7,15),(8,18),(9,13)]<br>
[(0,4),(1,2),(3,8),(5,7),(11,16),(12,14),(15,19),(17,18)]<br>
[(1,6),(2,12),(3,5),(4,11),(7,17),(8,15),(13,18),(14,16)]<br>
[(0,1),(2,6),(7,10),(9,12),(13,17),(18,19)]<br>
[(1,6),(5,9),(7,11),(8,12),(10,14),(13,18)]<br>
[(3,5),(4,7),(8,10),(9,11),(12,15),(14,16)]<br>
[(1,3),(2,4),(5,7),(6,10),(9,13),(12,14),(15,17),(16,18)]<br>
[(1,2),(3,4),(6,7),(8,9),(10,11),(12,13),(15,16),(17,18)]<br>
[(2,3),(4,6),(5,8),(7,9),(10,12),(11,14),(13,15),(16,17)]<br>
[(4,5),(6,8),(7,10),(9,12),(11,13),(14,15)]<br>
[(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16)]<br>
</p>Improved size over result (92) reported by Valsalam & Miikkulainen [<a href="#VM13">VM13</a>]</td><td>
Auto generated</td></tr>
<tr id="N20L93D11"><td>Sorting network for 20 inputs, 93 CEs, 11 layers:<br>
<p class="mono">[(0,12),(1,13),(2,14),(3,15),(4,16),(5,17),(6,18),(7,19),(8,10),(9,11)]<br>
[(0,2),(1,3),(4,6),(5,7),(8,9),(10,11),(12,14),(13,15),(16,18),(17,19)]<br>
[(0,1),(2,3),(4,5),(6,7),(12,13),(14,15),(16,17),(18,19)]<br>
[(0,4),(1,12),(2,16),(3,17),(5,8),(6,9),(7,18),(10,13),(11,14),(15,19)]<br>
[(1,6),(3,10),(4,5),(7,11),(8,12),(9,16),(13,18),(14,15)]<br>
[(0,4),(2,8),(3,9),(6,7),(10,16),(11,17),(12,13),(15,19)]<br>
[(1,4),(3,6),(5,8),(7,10),(9,12),(11,14),(13,16),(15,18)]<br>
[(2,3),(4,5),(6,8),(7,9),(10,12),(11,13),(14,15),(16,17)]<br>
[(2,4),(3,6),(5,7),(8,10),(9,11),(12,14),(13,16),(15,17)]<br>
[(1,2),(3,5),(6,7),(8,9),(10,11),(12,13),(14,16),(17,18)]<br>
[(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16)]<br>
</p>First 3 layers inspired by [<a href="#EM14">EM14</a>]</td><td>
Auto generated</td></tr>
<tr id="N21L99D15"><td>Sorting network for 21 inputs, 99 CEs, 15 layers:<br>
<p class="mono">[(0,1),(2,3),(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17),(18,19)]<br>
[(0,2),(1,3),(4,6),(5,7),(8,10),(9,11),(12,14),(13,15),(16,18),(17,19)]<br>
[(0,8),(1,9),(2,10),(3,11),(4,12),(5,13),(6,14),(7,15)]<br>
[(0,4),(1,5),(3,7),(6,20),(8,12),(9,13),(10,14),(15,19)]<br>
[(2,6),(3,18),(7,20)]<br>
[(2,16),(3,6),(5,18),(7,17),(11,20)]<br>
[(0,2),(3,8),(6,12),(7,10),(9,16),(11,15),(13,17),(14,18),(19,20)]<br>
[(1,7),(2,3),(4,9),(10,11),(13,16),(15,18),(17,19)]<br>
[(1,4),(5,10),(6,13),(7,8),(11,14),(12,16),(15,17),(18,19)]<br>
[(1,2),(3,4),(5,6),(10,12),(11,13),(14,16),(17,18)]<br>
[(2,3),(4,5),(6,9),(10,11),(12,13),(14,15),(16,17)]<br>
[(6,7),(8,9),(15,16)]<br>
[(4,6),(7,8),(9,12),(13,15)]<br>
[(3,4),(5,7),(8,10),(9,11),(12,14)]<br>
[(5,6),(7,8),(9,10),(11,12),(13,14)]<br>
</p>Improved size over result (102) reported by Valsalam & Miikkulainen [<a href="#VM13">VM13</a>], breaking 100 element barrier.</td><td>
Auto generated</td></tr>
<tr id="N21L100D12"><td>Sorting network for 21 inputs, 100 CEs, 12 layers:<br>
<p class="mono">[(0,7),(1,10),(3,5),(4,8),(6,13),(9,19),(11,14),(12,17),(15,16),(18,20)]<br>
[(0,11),(1,15),(2,12),(3,4),(5,8),(6,9),(7,14),(10,16),(13,19),(17,20)]<br>
[(0,6),(1,3),(2,18),(4,15),(5,10),(8,16),(11,17),(12,13),(14,20)]<br>
[(2,6),(5,12),(7,18),(8,14),(9,11),(10,17),(13,19),(16,20)]<br>
[(1,2),(4,7),(5,9),(6,17),(10,13),(11,12),(14,19),(15,18)]<br>
[(0,2),(3,6),(4,5),(7,10),(8,11),(9,15),(12,16),(13,18),(14,17),(19,20)]<br>
[(0,1),(2,3),(5,9),(6,12),(7,8),(11,14),(13,15),(16,19),(17,18)]<br>
[(1,2),(3,9),(6,13),(10,11),(12,15),(16,17),(18,19)]<br>
[(1,4),(2,5),(3,7),(6,10),(8,9),(11,12),(13,14),(17,18)]<br>
[(2,4),(5,6),(7,8),(9,11),(10,13),(12,15),(14,16)]<br>
[(3,4),(5,7),(6,8),(9,10),(11,13),(12,14),(15,16)]<br>
[(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17)]<br>
</p></td><td>
Auto generated</td></tr>
<tr id="N22L106D13"><td>Sorting network for 22 inputs, 106 CEs, 13 layers:<br>
<p class="mono">[(0,1),(2,3),(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17),(18,19),(20,21)]<br>
[(0,2),(1,3),(4,6),(5,7),(8,12),(9,13),(14,16),(15,17),(18,20),(19,21)]<br>
[(0,4),(1,5),(2,6),(3,7),(8,10),(9,12),(11,13),(14,18),(15,19),(16,20),(17,21)]<br>
[(0,14),(1,15),(2,18),(3,19),(4,16),(5,17),(6,20),(7,21),(9,11),(10,12)]<br>
[(2,8),(3,11),(6,9),(10,18),(12,15),(13,19)]<br>
[(0,2),(1,10),(3,16),(5,18),(6,14),(7,15),(8,12),(9,13),(11,20),(19,21)]<br>
[(2,6),(3,10),(4,8),(5,12),(9,16),(11,18),(13,17),(15,19)]<br>
[(1,4),(7,13),(8,14),(9,12),(17,20)]<br>
[(1,2),(3,8),(4,6),(7,11),(10,14),(13,18),(15,17),(19,20)]<br>
[(2,4),(5,10),(7,9),(11,16),(12,14),(17,19)]<br>
[(5,6),(7,8),(9,11),(10,12),(13,14),(15,16)]<br>
[(3,5),(6,7),(8,10),(9,12),(11,13),(14,15),(16,18)]<br>
[(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16),(17,18)]<br>
</p>Improved size over result (108) from Valsalam & Miikkulainen [<a href="#VM13">VM13</a>].</td><td>
Auto generated</td></tr>
<tr id="N22L107D12"><td>Sorting network for 22 inputs, 107 CEs, 12 layers:<br>
<p class="mono">[(0,1),(2,3),(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17),(18,19),(20,21)]<br>
[(0,2),(1,3),(4,6),(5,7),(8,10),(11,13),(14,16),(15,17),(18,20),(19,21)]<br>
[(0,4),(1,5),(2,6),(3,7),(8,12),(9,13),(14,18),(15,19),(16,20),(17,21)]<br>
[(0,14),(1,15),(2,18),(3,19),(4,16),(5,17),(6,20),(7,21),(9,11),(10,12)]<br>
[(0,8),(2,10),(4,14),(5,12),(6,15),(7,17),(9,16),(11,19),(13,21)]<br>
[(1,9),(2,4),(3,16),(5,18),(6,10),(7,13),(8,14),(11,15),(12,20),(17,19)]<br>
[(1,8),(3,11),(4,5),(7,12),(9,14),(10,18),(13,20),(16,17)]<br>
[(1,2),(3,5),(4,8),(6,9),(7,11),(10,14),(12,15),(13,17),(16,18),(19,20)]<br>
[(2,4),(3,6),(5,9),(7,10),(11,14),(12,16),(15,18),(17,19)]<br>
[(3,4),(5,7),(6,8),(9,11),(10,12),(13,15),(14,16),(17,18)]<br>
[(5,6),(7,8),(9,10),(11,12),(13,14),(15,16)]<br>
[(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17)]<br>
</p></td><td>
Auto generated</td></tr>
<tr id="N23L114D14"><td>Sorting network for 23 inputs, 114 CEs, 14 layers:<br>
<p class="mono">[(0,1),(2,3),(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17),(18,19),(20,21)]<br>
[(0,2),(1,3),(4,6),(5,7),(8,10),(9,11),(12,14),(13,15),(16,18),(17,19),(21,22)]<br>
[(0,4),(1,5),(2,6),(3,7),(8,12),(9,13),(10,14),(11,15),(17,21),(18,20),(19,22)]<br>
[(0,8),(1,9),(2,10),(3,11),(4,12),(5,13),(6,14),(7,15)]<br>
[(1,2),(5,18),(7,19),(9,16),(10,21),(12,20),(15,22)]<br>
[(5,9),(6,7),(10,18),(11,21),(12,17),(13,20),(14,15)]<br>
[(3,17),(6,16),(7,14),(8,12),(15,19),(20,21)]<br>
[(3,4),(5,8),(6,10),(9,12),(13,16),(14,15),(17,18),(19,21)]<br>
[(0,5),(1,8),(2,12),(3,9),(4,10),(7,13),(11,17),(14,16),(18,20)]<br>
[(2,6),(3,5),(4,8),(7,11),(10,12),(13,18),(14,17),(15,20)]<br>
[(1,3),(2,5),(6,9),(7,10),(11,13),(12,14),(15,18),(16,17),(19,20)]<br>
[(2,3),(4,6),(8,9),(11,12),(13,14),(15,16),(17,19)]<br>
[(3,4),(5,6),(7,8),(9,10),(12,13),(14,15),(17,18)]<br>
[(4,5),(6,7),(8,9),(10,11),(16,17)]<br>
</p>Reduction in size vs. 118 reported in [<a href="#Baddar09">Baddar09</a>]</td><td>
Auto generated</td></tr>
<tr id="N23L115D13"><td>Sorting network for 23 inputs, 115 CEs, 13 layers:<br>
<p class="mono">[(0,20),(1,12),(2,16),(4,6),(5,10),(7,21),(8,14),(9,15),(11,22),(13,18),(17,19)]<br>
[(0,3),(1,11),(2,7),(4,17),(5,13),(6,19),(8,9),(10,18),(12,22),(14,15),(16,21)]<br>
[(0,1),(2,4),(3,12),(5,8),(6,9),(7,10),(11,20),(13,16),(14,17),(15,18),(19,21)]<br>
[(2,5),(4,8),(6,11),(7,14),(9,16),(12,17),(15,19),(18,21)]<br>
[(1,8),(3,14),(4,7),(9,20),(10,12),(11,13),(15,22),(16,19)]<br>
[(0,7),(1,5),(3,4),(6,11),(8,15),(9,14),(10,13),(12,17),(18,22),(19,20)]<br>
[(0,2),(1,6),(4,7),(5,9),(8,10),(13,15),(14,18),(16,19),(17,22),(20,21)]<br>
[(2,3),(4,5),(6,8),(7,9),(10,11),(12,13),(14,16),(15,17),(18,19),(21,22)]<br>
[(1,2),(3,6),(4,10),(7,8),(9,11),(12,14),(13,19),(15,16),(17,20)]<br>
[(2,3),(5,10),(6,7),(8,9),(13,18),(14,15),(16,17),(20,21)]<br>
[(3,4),(5,7),(10,12),(11,13),(16,18),(19,20)]<br>
[(4,6),(8,10),(9,12),(11,14),(13,15),(17,19)]<br>
[(5,6),(7,8),(9,10),(11,12),(13,14),(15,16),(17,18)]<br>
</p>Obtained by removing highest input from 24 inputs case with 13 layers.</td><td>
Auto generated</td></tr>
<tr id="N23L116D12"><td>Sorting network for 23 inputs, 116 CEs, 12 layers:<br>
<p class="mono">[(0,1),(2,3),(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17),(18,19),(20,21)]<br>
[(0,2),(1,3),(4,6),(5,7),(8,10),(9,11),(12,14),(13,15),(17,19),(18,20),(21,22)]<br>
[(0,4),(1,5),(2,6),(3,7),(8,12),(9,13),(10,14),(11,15),(16,21),(17,22)]<br>
[(1,10),(2,9),(3,11),(6,19),(12,17),(14,22),(16,18),(20,21)]<br>
[(0,16),(1,2),(3,21),(4,17),(5,14),(6,13),(7,22),(9,18),(10,20),(15,19)]<br>
[(1,10),(2,9),(3,17),(4,12),(5,18),(6,20),(7,15),(8,16),(11,14),(13,21),(19,22)]<br>
[(0,8),(1,4),(2,10),(3,9),(5,6),(11,21),(12,16),(13,20),(14,15),(17,18)]<br>
[(2,8),(3,5),(4,12),(6,9),(7,11),(10,16),(13,17),(15,21),(18,20)]<br>
[(1,2),(4,8),(5,10),(6,12),(7,13),(9,16),(11,18),(14,17),(15,19)]<br>
[(2,4),(3,5),(6,8),(7,9),(10,12),(11,13),(14,16),(15,20),(17,18),(19,21)]<br>
[(3,6),(5,8),(7,10),(9,12),(11,14),(13,16),(15,17),(18,20)]<br>
[(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16),(17,18),(19,20)]<br>
</p></td><td>
Auto generated</td></tr>
<tr id="N24L120D13"><td>Sorting network for 24 inputs, 120 CEs, 13 layers:<br>
<p class="mono">[(0,20),(1,12),(2,16),(3,23),(4,6),(5,10),(7,21),(8,14),(9,15),(11,22),(13,18),(17,19)]<br>
[(0,3),(1,11),(2,7),(4,17),(5,13),(6,19),(8,9),(10,18),(12,22),(14,15),(16,21),(20,23)]<br>
[(0,1),(2,4),(3,12),(5,8),(6,9),(7,10),(11,20),(13,16),(14,17),(15,18),(19,21),(22,23)]<br>
[(2,5),(4,8),(6,11),(7,14),(9,16),(12,17),(15,19),(18,21)]<br>
[(1,8),(3,14),(4,7),(9,20),(10,12),(11,13),(15,22),(16,19)]<br>
[(0,7),(1,5),(3,4),(6,11),(8,15),(9,14),(10,13),(12,17),(16,23),(18,22),(19,20)]<br>
[(0,2),(1,6),(4,7),(5,9),(8,10),(13,15),(14,18),(16,19),(17,22),(21,23)]<br>
[(2,3),(4,5),(6,8),(7,9),(10,11),(12,13),(14,16),(15,17),(18,19),(20,21)]<br>
[(1,2),(3,6),(4,10),(7,8),(9,11),(12,14),(13,19),(15,16),(17,20),(21,22)]<br>
[(2,3),(5,10),(6,7),(8,9),(13,18),(14,15),(16,17),(20,21)]<br>
[(3,4),(5,7),(10,12),(11,13),(16,18),(19,20)]<br>
[(4,6),(8,10),(9,12),(11,14),(13,15),(17,19)]<br>
[(5,6),(7,8),(9,10),(11,12),(13,14),(15,16),(17,18)]<br>
</p>Reduction in size vs. 123 reported in [<a href="#Baddar09">Baddar09</a>]</td><td>
Auto generated</td></tr>
<tr id="N24L122D12"><td>Sorting network for 24 inputs, 122 CEs, 12 layers:<br>
<p class="mono">[(0,1),(2,3),(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17),(18,19),(20,21),(22,23)]<br>
[(0,2),(1,3),(4,6),(5,7),(8,10),(9,11),(12,14),(13,15),(16,18),(17,19),(20,22),(21,23)]<br>
[(0,4),(1,5),(2,6),(3,7),(8,12),(9,13),(10,14),(11,15),(16,20),(17,21),(18,22),(19,23)]<br>
[(0,16),(1,18),(2,17),(3,19),(4,20),(5,22),(6,21),(7,23),(9,10),(13,14)]<br>
[(2,10),(3,11),(5,18),(6,14),(7,15),(8,16),(9,17),(12,20),(13,21)]<br>
[(0,8),(1,9),(2,12),(3,20),(4,16),(5,13),(6,17),(7,19),(10,18),(11,21),(14,22),(15,23)]<br>
[(1,8),(3,16),(4,12),(5,10),(6,9),(7,20),(11,19),(13,18),(14,17),(15,22)]<br>
[(2,4),(3,5),(7,13),(9,12),(10,16),(11,14),(18,20),(19,21)]<br>
[(1,2),(4,8),(5,9),(6,10),(7,11),(12,16),(13,17),(14,18),(15,19),(21,22)]<br>
[(2,4),(3,8),(5,6),(7,9),(10,12),(11,13),(14,16),(15,20),(17,18),(19,21)]<br>
[(3,5),(6,8),(7,10),(9,12),(11,14),(13,16),(15,17),(18,20)]<br>
[(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16),(17,18),(19,20)]<br>
</p></td><td>
Auto generated</td></tr>
<tr id="N25L130D15"><td>Sorting network for 25 inputs, 130 CEs, 15 layers:<br>
<p class="mono">[(0,1),(2,3),(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17),(18,19),(20,21),(22,23)]<br>
[(0,2),(1,3),(4,6),(5,7),(8,10),(9,11),(12,14),(13,15),(16,18),(17,19),(21,22),(23,24)]<br>
[(0,4),(1,5),(2,6),(3,7),(8,12),(9,13),(10,14),(11,15),(18,21),(20,23),(22,24)]<br>
[(0,8),(1,9),(2,10),(3,11),(4,12),(5,13),(6,14),(7,15),(16,20),(17,22),(19,24),(21,23)]<br>
[(1,18),(3,21),(5,23),(6,19),(11,14),(15,24)]<br>
[(1,16),(3,17),(6,9),(7,11),(13,19),(14,23)]<br>
[(0,1),(2,16),(3,8),(7,20),(10,13),(11,22),(15,23)]<br>
[(1,2),(5,10),(7,18),(11,21),(15,20),(19,22)]<br>
[(4,7),(5,6),(9,18),(10,17),(11,12),(13,21),(14,15),(19,20),(22,23)]<br>
[(3,4),(7,8),(9,10),(11,16),(12,17),(13,18),(19,21),(20,22)]<br>
[(1,3),(2,4),(5,11),(6,16),(7,9),(8,10),(12,13),(14,19),(15,18)]<br>
[(2,3),(5,7),(6,9),(8,11),(10,16),(12,14),(15,17)]<br>
[(3,5),(4,6),(7,8),(9,11),(10,12),(13,14),(15,16),(17,18)]<br>
[(4,7),(6,8),(9,10),(11,12),(13,15),(14,16),(17,19),(18,21)]<br>
[(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17),(18,19),(20,21)]<br>
</p>Improved size vs. <a href="https://en.wikipedia.org/wiki/Batcher_odd%E2%80%93even_mergesort">Batcher odd-even merge</a>.</td><td>
Auto generated</td></tr>
<tr id="N25L131D13"><td>Sorting network for 25 inputs, 131 CEs, 13 layers:<br>
<p class="mono">[(0,1),(2,3),(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17),(18,19),(20,21),(22,23)]<br>
[(0,2),(1,3),(4,6),(5,7),(8,10),(9,11),(12,14),(13,15),(16,18),(17,19),(20,22),(21,24)]<br>
[(0,4),(1,5),(2,6),(3,7),(8,12),(9,13),(10,14),(11,15),(16,20),(21,22),(23,24)]<br>
[(0,8),(1,12),(2,10),(3,14),(4,9),(5,13),(6,11),(7,15),(17,22),(18,21),(19,24)]<br>
[(1,18),(3,9),(5,17),(6,20),(7,13),(11,14),(12,22),(15,24),(21,23)]<br>
[(1,16),(3,12),(5,21),(6,18),(7,11),(10,17),(14,23),(19,20)]<br>
[(0,1),(2,5),(4,16),(6,8),(7,18),(9,21),(10,14),(11,13),(12,19),(15,23),(20,22)]<br>
[(1,2),(3,5),(4,6),(7,9),(8,12),(10,16),(11,20),(13,22),(14,17),(15,18),(19,21)]<br>
[(1,4),(2,6),(3,7),(5,9),(8,10),(11,14),(12,16),(13,17),(15,19),(18,20),(22,23)]<br>
[(2,4),(3,8),(5,10),(7,12),(9,16),(11,15),(13,19),(14,21),(17,18),(20,22)]<br>
[(3,4),(5,8),(6,7),(9,12),(10,11),(13,16),(14,15),(17,19),(18,21)]<br>
[(5,6),(7,8),(9,10),(11,12),(13,14),(15,16),(17,18),(20,21)]<br>
[(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17),(18,19)]<br>
</p>Improved size and depth over obtainable metrics by <a href="https://en.wikipedia.org/wiki/Batcher_odd%E2%80%93even_mergesort">Batcher odd-even merge</a>. The existence of a 13 layer network was conjectured in the conclusion of [<a href="#Ehlers17">Ehlers17</a>].</td><td>
Auto generated</td></tr>
<tr id="N26L139D14"><td>Sorting network for 26 inputs, 139 CEs, 14 layers:<br>
<p class="mono">[(0,1),(2,3),(4,21),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16),(17,18),(19,20),(22,23),(24,25)]<br>
[(0,24),(1,25),(3,21),(4,22),(5,7),(6,8),(9,11),(10,12),(13,15),(14,16),(17,19),(18,20)]<br>
[(0,4),(2,22),(3,23),(5,9),(6,10),(7,11),(8,12),(13,17),(14,18),(15,19),(16,20),(21,25)]<br>
[(0,2),(1,3),(4,21),(5,13),(6,14),(7,15),(8,16),(9,17),(10,18),(11,19),(12,20),(22,24),(23,25)]<br>
[(0,5),(1,7),(2,4),(3,10),(15,22),(18,24),(20,25),(21,23)]<br>
[(2,9),(3,7),(4,14),(5,13),(6,15),(10,19),(11,21),(12,20),(16,23),(18,22)]<br>
[(1,5),(2,6),(3,15),(7,17),(8,18),(10,22),(11,13),(12,14),(19,23),(20,24)]<br>
[(1,2),(4,7),(5,11),(8,9),(10,12),(13,15),(14,20),(16,17),(18,21),(23,24)]<br>
[(3,8),(4,6),(7,16),(9,18),(10,13),(12,15),(17,22),(19,21)]<br>
[(4,5),(6,11),(7,9),(14,19),(16,18),(20,21)]<br>
[(2,4),(3,6),(7,10),(8,11),(9,12),(13,16),(14,17),(15,18),(19,22),(21,23)]<br>
[(3,4),(5,8),(6,7),(9,10),(11,13),(12,14),(15,16),(17,20),(18,19),(21,22)]<br>
[(5,6),(7,8),(9,11),(10,13),(12,15),(14,16),(17,18),(19,20)]<br>
[(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17),(18,19),(20,21)]<br>
</p>Improved size over <a href="https://en.wikipedia.org/wiki/Batcher_odd%E2%80%93even_mergesort">Batcher odd-even merge</a></td><td>
Auto generated</td></tr>
<tr id="N26L141D13"><td>Sorting network for 26 inputs, 141 CEs, 13 layers:<br>
<p class="mono">[(0,1),(2,3),(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17),(18,19),(20,21),(22,23),(24,25)]<br>
[(0,2),(1,3),(4,6),(5,7),(8,10),(9,11),(14,16),(15,17),(18,20),(19,21),(22,24),(23,25)]<br>
[(0,4),(1,5),(2,6),(3,7),(8,14),(9,16),(10,13),(11,17),(12,15),(18,22),(19,23),(20,24),(21,25)]<br>
[(0,18),(1,19),(2,20),(3,21),(4,22),(5,23),(6,24),(7,25),(8,12),(10,14),(11,15),(13,17)]<br>
[(1,18),(2,10),(3,20),(4,8),(5,22),(6,14),(7,24),(9,12),(11,19),(13,16),(15,23),(17,21)]<br>
[(0,4),(1,9),(3,13),(5,15),(6,18),(7,19),(8,11),(10,20),(12,22),(14,17),(16,24),(21,25)]<br>
[(2,4),(3,11),(5,9),(10,12),(13,15),(14,22),(16,20),(21,23)]<br>
[(1,4),(3,8),(6,10),(7,13),(9,11),(12,18),(14,16),(15,19),(17,22),(21,24)]<br>
[(1,2),(3,6),(4,5),(7,12),(8,10),(9,14),(11,16),(13,18),(15,17),(19,22),(20,21),(23,24)]<br>
[(2,3),(4,6),(5,10),(7,9),(11,13),(12,14),(15,20),(16,18),(19,21),(22,23)]<br>
[(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16),(17,18),(19,20),(21,22)]<br>
[(5,7),(6,8),(9,11),(10,12),(13,15),(14,16),(17,19),(18,20)]<br>
[(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17),(18,19),(20,21)]<br>
</p>Improved depth from 14 that could be achieved by <a href="https://en.wikipedia.org/wiki/Batcher_odd%E2%80%93even_mergesort">Batcher odd-even merge</a></td><td>
Auto generated</td></tr>
<tr id="N27L147D16"><td>Sorting network for 27 inputs, 147 CEs, 16 layers:<br>
<p class="mono">[(0,1),(2,3),(4,5),(6,7),(8,9),(10,11),(12,14),(15,16),(17,18),(19,20),(21,22),(23,24),(25,26)]<br>
[(0,2),(1,3),(4,6),(5,7),(8,10),(9,11),(12,13),(15,17),(16,18),(19,21),(20,22),(23,25),(24,26)]<br>
[(0,23),(1,24),(2,25),(3,26),(4,8),(5,9),(6,10),(7,11),(13,14),(15,19),(16,20),(17,21),(18,22)]<br>
[(0,4),(1,6),(2,19),(3,20),(5,13),(9,21),(11,14),(12,16),(17,23),(18,24),(22,26)]<br>
[(5,17),(6,16),(7,22),(9,25),(10,24),(12,15),(13,20),(14,26)]<br>
[(1,12),(4,15),(7,23),(10,19),(11,16),(13,18),(20,24),(22,25)]<br>
[(0,1),(6,12),(8,11),(9,15),(10,17),(14,24),(16,21),(18,19)]<br>
[(1,4),(2,8),(3,11),(12,15),(14,20),(16,22),(21,25)]<br>
[(2,5),(3,17),(8,13),(11,23),(21,22),(24,25)]<br>
[(1,2),(3,10),(5,6),(7,13),(11,15),(14,21),(18,23),(20,22)]<br>
[(4,5),(6,9),(7,8),(13,17),(14,16),(19,23),(22,24)]<br>
[(2,4),(3,6),(5,7),(8,12),(9,10),(11,13),(14,18),(15,17),(16,19),(21,23)]<br>
[(3,5),(6,8),(7,9),(10,12),(11,14),(13,16),(15,18),(17,19),(20,21),(22,23)]<br>
[(5,6),(8,11),(9,10),(12,14),(13,15),(17,18),(19,21)]<br>
[(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17),(18,20),(21,22)]<br>
[(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16),(17,18),(19,20)]<br>
</p>Improved size compared to 150 that could be obtained by <a href="https://en.wikipedia.org/wiki/Batcher_odd%E2%80%93even_mergesort">Batcher odd-even merge</a></td><td>
Auto generated</td></tr>
<tr id="N27L148D14"><td>Sorting network for 27 inputs, 148 CEs, 14 layers:<br>
<p class="mono">[(0,17),(1,20),(2,23),(3,24),(4,9),(5,18),(6,16),(7,13),(8,15),(10,14),(11,21),(19,26),(22,25)]<br>
[(0,4),(1,8),(2,19),(3,7),(5,6),(9,17),(10,11),(12,25),(13,24),(14,21),(15,20),(16,18),(23,26)]<br>
[(0,2),(1,3),(4,23),(5,10),(6,14),(7,8),(9,19),(11,16),(12,22),(13,15),(17,26),(18,21),(20,24)]<br>
[(1,5),(2,12),(3,6),(4,9),(7,11),(8,18),(10,13),(14,15),(16,20),(19,23),(21,24),(25,26)]<br>
[(0,2),(3,7),(4,22),(5,10),(8,13),(9,25),(11,14),(15,18),(20,21)]<br>
[(0,1),(2,3),(4,5),(6,14),(7,10),(9,12),(11,17),(19,22),(23,25)]<br>
[(1,2),(3,6),(5,11),(7,9),(8,19),(12,18),(14,26),(16,23),(17,22),(20,25)]<br>
[(3,5),(6,16),(9,14),(10,12),(13,17),(15,23),(18,25),(19,20),(21,22),(24,26)]<br>
[(2,10),(5,9),(6,8),(11,13),(12,14),(15,16),(17,21),(22,24)]<br>
[(2,7),(3,6),(8,10),(9,11),(12,15),(13,19),(14,16),(17,20),(18,21),(22,23),(24,25)]<br>
[(4,7),(5,8),(6,9),(10,11),(12,13),(14,17),(15,19),(16,20),(18,22),(23,24)]<br>
[(1,4),(3,7),(5,6),(8,10),(9,12),(11,13),(14,15),(16,17),(18,19),(20,21)]<br>
[(2,4),(6,7),(8,9),(10,12),(11,14),(13,15),(16,18),(17,19),(20,22),(21,23)]<br>
[(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16),(17,18),(19,20),(21,22)]<br>
</p></td><td>
Auto generated</td></tr>
<tr id="N28L155D14"><td>Sorting network for 28 inputs, 155 CEs, 14 layers:<br>
<p class="mono">[(0,1),(2,3),(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17),(18,19),(20,21),(22,23),(24,25),(26,27)]<br>
[(0,2),(1,3),(4,6),(5,7),(8,10),(9,11),(12,14),(13,15),(16,18),(17,19),(20,22),(21,23),(24,26),(25,27)]<br>
[(0,4),(1,5),(2,6),(3,7),(8,12),(9,13),(14,18),(15,19),(20,24),(21,25),(22,26),(23,27)]<br>
[(0,20),(1,21),(2,22),(3,23),(4,24),(5,25),(6,26),(7,27),(9,17),(10,18),(11,15),(12,16)]<br>
[(1,2),(4,20),(5,6),(7,23),(8,12),(9,16),(10,14),(11,18),(13,17),(15,19),(21,22),(25,26)]<br>
[(0,8),(1,9),(2,12),(3,5),(4,10),(6,16),(7,13),(11,21),(14,20),(15,25),(17,23),(18,26),(19,27),(22,24)]<br>
[(2,4),(3,7),(5,17),(8,14),(9,11),(10,22),(13,19),(16,18),(20,24),(23,25)]<br>
[(1,8),(3,9),(5,11),(6,10),(7,15),(12,20),(16,22),(17,21),(18,24),(19,26)]<br>
[(1,2),(4,6),(5,9),(10,16),(11,17),(12,14),(13,15),(18,22),(21,23),(25,26)]<br>
[(4,8),(6,12),(7,11),(10,14),(13,17),(15,21),(16,20),(19,23)]<br>
[(2,4),(6,8),(7,16),(9,14),(10,12),(11,20),(13,18),(15,17),(19,21),(23,25)]<br>
[(3,10),(5,12),(7,9),(11,13),(14,16),(15,22),(17,24),(18,20)]<br>
[(3,6),(5,8),(7,10),(9,12),(11,14),(13,16),(15,18),(17,20),(19,22),(21,24)]<br>
[(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16),(17,18),(19,20),(21,22),(23,24)]<br>
</p>Improved size over 156 that could be obtained by <a href="https://en.wikipedia.org/wiki/Batcher_odd%E2%80%93even_mergesort">Batcher odd-even merge</a></td><td>
Auto generated</td></tr>
<tr id="N29L164D15"><td>Sorting network for 29 inputs, 164 CEs, 15 layers:<br>
<p class="mono">[(0,1),(2,3),(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,28),(17,26),(18,25),(19,23),(21,27),(22,24)]<br>
[(0,2),(1,3),(4,6),(5,7),(8,10),(9,11),(12,14),(13,15),(17,22),(18,19),(20,27),(23,25),(24,26)]<br>
[(0,4),(1,5),(2,6),(3,7),(8,12),(9,13),(10,14),(11,15),(16,20),(17,18),(19,22),(23,24),(25,26),(27,28)]<br>
[(0,8),(1,9),(2,10),(3,11),(4,12),(5,13),(6,14),(7,15),(16,18),(20,22),(21,25),(24,27),(26,28)]<br>
[(1,8),(2,24),(4,19),(5,20),(6,21),(7,27),(9,18),(10,23),(11,26),(13,22),(14,25),(15,28),(16,17)]<br>
[(0,6),(2,4),(3,24),(5,10),(12,19),(13,18),(14,21),(15,25),(20,23),(26,27)]<br>
[(0,16),(1,6),(3,12),(4,8),(5,17),(7,24),(14,20),(15,26),(18,21),(19,23),(25,27)]<br>
[(1,5),(2,16),(3,10),(6,9),(7,18),(8,17),(11,19),(13,14),(15,22),(21,23),(25,26)]<br>
[(1,2),(3,5),(4,8),(6,16),(7,11),(9,17),(10,12),(14,20),(15,18),(19,24),(22,27)]<br>
[(4,6),(9,16),(10,13),(11,19),(12,14),(20,21),(22,26),(23,24)]<br>
[(2,4),(3,6),(7,16),(8,9),(11,17),(15,19),(18,23),(24,25)]<br>
[(3,4),(5,9),(7,10),(11,13),(12,16),(14,17),(15,20),(19,21),(22,24)]<br>
[(5,8),(6,7),(9,12),(10,11),(13,14),(15,16),(17,20),(18,19),(21,23),(24,25)]<br>
[(5,6),(7,8),(9,10),(11,12),(13,15),(14,16),(17,18),(19,20),(21,22)]<br>
[(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17),(18,19),(20,21),(22,23)]<br>
</p>Improved size over 165 that could be obtained by <a href="https://en.wikipedia.org/wiki/Batcher_odd%E2%80%93even_mergesort">Batcher odd-even merge</a></td><td>
Auto generated</td></tr>
<tr id="N29L166D14"><td>Sorting network for 29 inputs, 166 CEs, 14 layers:<br>
<p class="mono">[(0,1),(2,3),(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17),(18,19),(20,21),(22,23),(24,25),(26,27)]<br>
[(0,2),(1,3),(4,6),(5,7),(8,10),(9,11),(12,14),(13,15),(16,18),(17,19),(20,22),(21,23),(24,26),(25,27)]<br>
[(0,4),(1,5),(2,6),(3,7),(8,12),(9,13),(10,14),(11,15),(16,20),(17,21),(18,22),(19,23),(24,28)]<br>
[(0,8),(1,9),(2,10),(3,11),(4,12),(5,13),(6,14),(7,15),(16,24),(17,25),(18,26),(19,27),(20,28)]<br>
[(0,16),(1,8),(2,4),(3,12),(5,10),(6,9),(7,14),(11,13),(17,24),(18,20),(19,28),(21,26),(22,25),(23,27)]<br>
[(1,2),(3,5),(4,8),(6,22),(7,11),(9,25),(10,12),(13,14),(17,18),(19,21),(20,24),(26,28)]<br>
[(1,17),(2,18),(3,19),(4,20),(5,10),(7,23),(8,24),(11,27),(12,28),(13,25),(21,26)]<br>
[(3,17),(4,16),(5,21),(6,18),(7,9),(8,20),(10,26),(11,23),(14,28),(15,27),(22,24)]<br>
[(1,4),(3,8),(5,16),(7,17),(9,21),(10,22),(11,19),(12,20),(14,24),(15,26),(23,28)]<br>
[(2,5),(7,8),(9,18),(11,17),(12,16),(13,22),(14,20),(15,19),(23,24)]<br>
[(2,4),(6,12),(9,16),(10,11),(13,17),(14,18),(15,22),(19,25),(20,21)]<br>
[(5,6),(8,12),(9,10),(11,13),(14,16),(15,17),(18,20),(19,23),(21,22),(25,26)]<br>
[(3,5),(6,7),(8,9),(10,12),(11,14),(13,16),(15,18),(17,20),(19,21),(22,23),(24,25),(26,28)]<br>
[(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16),(17,18),(19,20),(21,22),(23,24),(25,26),(27,28)]<br>
</p>Obtained by removing 3 inputs from the 32 input network with 185 elements and 14 layers.</td><td>
Auto generated</td></tr>
<tr id="N30L172D14"><td>Sorting network for 30 inputs, 172 CEs, 14 layers:<br>
<p class="mono">[(0,1),(2,3),(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17),(18,19),(20,21),(22,23),(24,25),(26,27),(28,29)]<br>
[(0,2),(1,3),(4,6),(5,7),(8,10),(9,11),(13,15),(14,16),(18,20),(19,21),(22,24),(23,25),(26,28),(27,29)]<br>
[(0,4),(1,5),(2,6),(3,7),(8,14),(9,17),(10,16),(12,20),(13,19),(15,21),(22,26),(23,27),(24,28),(25,29)]<br>
[(0,8),(1,9),(2,14),(3,17),(4,10),(5,11),(6,16),(12,26),(13,23),(15,27),(18,24),(19,25),(20,28),(21,29)]<br>
[(1,13),(2,12),(3,15),(4,18),(5,19),(6,20),(7,21),(8,22),(9,23),(10,24),(11,25),(14,26),(16,28),(17,27)]<br>
[(0,4),(2,8),(3,13),(5,9),(6,22),(7,23),(10,12),(11,15),(14,18),(16,26),(17,19),(20,24),(21,27),(25,29)]<br>
[(0,2),(1,14),(3,5),(4,8),(9,13),(11,17),(12,18),(15,28),(16,20),(21,25),(24,26),(27,29)]<br>
[(2,4),(5,9),(6,14),(7,13),(8,10),(15,23),(16,22),(19,21),(20,24),(25,27)]<br>
[(6,8),(7,11),(10,14),(12,16),(13,17),(15,19),(18,22),(21,23)]<br>
[(4,6),(7,9),(8,10),(11,13),(12,14),(15,17),(16,18),(19,21),(20,22),(23,25)]<br>
[(1,8),(3,18),(5,20),(7,22),(9,24),(10,12),(11,26),(13,15),(14,16),(17,19),(21,28)]<br>
[(1,2),(3,10),(5,12),(7,14),(9,16),(11,18),(13,20),(15,22),(17,24),(19,26),(27,28)]<br>
[(2,4),(3,6),(5,8),(7,10),(9,12),(11,14),(13,16),(15,18),(17,20),(19,22),(21,24),(23,26),(25,27)]<br>
[(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16),(17,18),(19,20),(21,22),(23,24),(25,26)]<br>
</p>Combines best known size and depth. An interesting pattern emerged through evolution in the last 4 layers: each layer "specializes" in elements bridging vertical distances of respectively 15, 7, 3 and 1, equally spaced with a stride of 2. This pattern is also typical for "pairwise" sorting networks [<a href="#Par92">Par92</a>].</td><td>
Auto generated</td></tr>
<tr id="N31L180D14"><td>Sorting network for 31 inputs, 180 CEs, 14 layers:<br>
<p class="mono">[(0,1),(2,3),(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17),(18,19),(20,21),(22,23),(24,25),(26,27),(28,29)]<br>
[(0,2),(1,3),(4,6),(5,7),(8,10),(9,11),(12,14),(13,15),(16,18),(17,19),(20,22),(21,23),(24,26),(25,27),(28,30)]<br>
[(0,4),(1,5),(2,6),(3,7),(8,12),(9,13),(10,14),(11,15),(16,20),(17,21),(18,22),(19,23),(24,28),(25,29),(26,30)]<br>
[(0,8),(1,9),(2,10),(3,11),(4,12),(5,13),(6,14),(7,15),(16,24),(17,25),(18,26),(19,27),(20,28),(21,29),(22,30)]<br>
[(0,16),(1,8),(2,4),(3,12),(5,10),(6,9),(7,14),(11,13),(17,24),(18,20),(19,28),(21,26),(22,25),(23,30),(27,29)]<br>
[(1,2),(3,5),(4,8),(6,22),(7,11),(9,25),(10,12),(13,14),(17,18),(19,21),(20,24),(23,27),(26,28),(29,30)]<br>
[(1,17),(2,18),(3,19),(4,20),(5,10),(7,23),(8,24),(11,27),(12,28),(13,29),(14,30),(21,26)]<br>
[(3,17),(4,16),(5,21),(6,18),(7,9),(8,20),(10,26),(11,23),(13,25),(14,28),(15,27),(22,24)]<br>
[(1,4),(3,8),(5,16),(7,17),(9,21),(10,22),(11,19),(12,20),(14,24),(15,26),(23,28),(27,30)]<br>
[(2,5),(7,8),(9,18),(11,17),(12,16),(13,22),(14,20),(15,19),(23,24),(26,29)]<br>
[(2,4),(6,12),(9,16),(10,11),(13,17),(14,18),(15,22),(19,25),(20,21),(27,29)]<br>
[(5,6),(8,12),(9,10),(11,13),(14,16),(15,17),(18,20),(19,23),(21,22),(25,26)]<br>
[(3,5),(6,7),(8,9),(10,12),(11,14),(13,16),(15,18),(17,20),(19,21),(22,23),(24,25),(26,28)]<br>
[(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16),(17,18),(19,20),(21,22),(23,24),(25,26),(27,28)]<br>
</p>Obtained by removing one input from the network with 32 inputs, 185 elements and 14 layers.</td><td>
Auto generated</td></tr>
<tr id="N32L185D14"><td>Sorting network for 32 inputs, 185 CEs, 14 layers:<br>
<p class="mono">[(0,1),(2,3),(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17),(18,19),(20,21),(22,23),(24,25),(26,27),(28,29),(30,31)]<br>
[(0,2),(1,3),(4,6),(5,7),(8,10),(9,11),(12,14),(13,15),(16,18),(17,19),(20,22),(21,23),(24,26),(25,27),(28,30),(29,31)]<br>
[(0,4),(1,5),(2,6),(3,7),(8,12),(9,13),(10,14),(11,15),(16,20),(17,21),(18,22),(19,23),(24,28),(25,29),(26,30),(27,31)]<br>
[(0,8),(1,9),(2,10),(3,11),(4,12),(5,13),(6,14),(7,15),(16,24),(17,25),(18,26),(19,27),(20,28),(21,29),(22,30),(23,31)]<br>
[(0,16),(1,8),(2,4),(3,12),(5,10),(6,9),(7,14),(11,13),(15,31),(17,24),(18,20),(19,28),(21,26),(22,25),(23,30),(27,29)]<br>
[(1,2),(3,5),(4,8),(6,22),(7,11),(9,25),(10,12),(13,14),(17,18),(19,21),(20,24),(23,27),(26,28),(29,30)]<br>
[(1,17),(2,18),(3,19),(4,20),(5,10),(7,23),(8,24),(11,27),(12,28),(13,29),(14,30),(21,26)]<br>
[(3,17),(4,16),(5,21),(6,18),(7,9),(8,20),(10,26),(11,23),(13,25),(14,28),(15,27),(22,24)]<br>
[(1,4),(3,8),(5,16),(7,17),(9,21),(10,22),(11,19),(12,20),(14,24),(15,26),(23,28),(27,30)]<br>
[(2,5),(7,8),(9,18),(11,17),(12,16),(13,22),(14,20),(15,19),(23,24),(26,29)]<br>
[(2,4),(6,12),(9,16),(10,11),(13,17),(14,18),(15,22),(19,25),(20,21),(27,29)]<br>
[(5,6),(8,12),(9,10),(11,13),(14,16),(15,17),(18,20),(19,23),(21,22),(25,26)]<br>
[(3,5),(6,7),(8,9),(10,12),(11,14),(13,16),(15,18),(17,20),(19,21),(22,23),(24,25),(26,28)]<br>
[(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16),(17,18),(19,20),(21,22),(23,24),(25,26),(27,28)]<br>
</p>This network was obtained by evolution using a fixed prefix in its first 4 layers. Its size and depth combine the best results that can be achieved using a <a href="https://en.wikipedia.org/wiki/Batcher_odd%E2%80%93even_mergesort">Batcher odd-even merge</a> of either twice the 16 input network with 60 CEs and 10 layers or twice the 16 input network with 61 CEs and 9 layers.</td><td>
Auto generated</td></tr>
<tr id="N33L199D16"><td>Sorting network for 33 inputs, 199 CEs, 16 layers:<br>
<p class="mono">[(0,1),(2,3),(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17),(18,19),(20,21),(22,23),(24,25),(26,27),(28,29),(30,31)]<br>
[(0,2),(1,3),(4,6),(5,7),(8,10),(9,11),(12,14),(13,15),(16,18),(17,19),(20,22),(21,23),(24,26),(25,27),(28,30),(29,31)]<br>
[(0,4),(1,5),(2,6),(3,7),(8,12),(9,13),(10,14),(11,15),(16,20),(17,21),(18,22),(19,23),(24,28),(25,29),(26,30),(27,31)]<br>
[(0,8),(1,9),(2,10),(3,11),(4,12),(5,13),(6,14),(7,15),(16,24),(17,25),(18,26),(19,27),(20,28),(21,29),(22,30),(23,31)]<br>
[(0,16),(1,17),(2,18),(3,19),(4,20),(5,21),(6,22),(7,23),(8,24),(9,25),(10,26),(11,27),(12,28),(13,29),(14,30),(15,31)]<br>
[(1,4),(2,16),(3,20),(5,18),(6,17),(7,22),(9,24),(10,12),(11,28),(13,26),(14,25),(15,29),(19,21),(23,32),(27,30)]<br>
[(1,2),(3,9),(4,16),(6,10),(7,19),(11,17),(12,24),(13,23),(15,27),(22,26),(25,28),(29,30)]<br>
[(3,6),(7,12),(9,18),(10,20),(13,14),(15,28),(17,22),(21,25),(27,32)]<br>
[(5,13),(6,16),(9,10),(12,20),(14,19),(15,23),(25,26),(30,32)]<br>
[(5,8),(11,13),(14,18),(15,21),(19,22),(23,27),(31,32)]<br>
[(4,5),(7,11),(8,16),(12,14),(13,24),(15,17),(18,20),(19,21),(22,28),(23,25),(27,29)]<br>
[(1,4),(3,5),(6,8),(7,9),(10,11),(13,15),(17,24),(22,23),(26,27),(29,30)]<br>
[(0,1),(2,6),(8,9),(11,16),(12,13),(14,17),(15,18),(19,22),(20,24),(25,26)]<br>
[(2,4),(5,8),(6,7),(9,11),(10,12),(13,16),(14,15),(17,20),(18,19),(21,24),(23,25),(26,28)]<br>
[(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16),(17,18),(19,20),(21,22),(23,24),(25,26),(27,28)]<br>
[(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17),(18,19),(20,21),(22,23),(24,25),(28,29)]<br>
</p>Improved size over Batcher and Van Voorhis merges</td><td>
Auto generated</td></tr>
<tr id="N33L200D15"><td>Sorting network for 33 inputs, 200 CEs, 15 layers:<br>
<p class="mono">[(0,1),(2,3),(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17),(18,19),(20,21),(22,23),(24,25),(26,27),(28,29),(30,31)]<br>
[(0,2),(1,3),(4,6),(5,7),(8,10),(9,11),(12,14),(13,15),(16,18),(17,19),(20,22),(21,23),(24,26),(25,27),(28,30),(29,31)]<br>
[(0,4),(1,5),(2,6),(3,7),(8,12),(9,13),(10,14),(11,15),(16,20),(17,21),(18,22),(19,23),(24,28),(25,29),(26,30),(27,31)]<br>
[(0,8),(1,9),(2,10),(3,11),(4,12),(5,13),(6,14),(7,15),(16,24),(17,25),(18,26),(19,27),(20,28),(21,29),(22,30),(23,31)]<br>
[(0,16),(1,17),(2,18),(3,19),(4,20),(5,21),(6,22),(7,23),(8,24),(9,25),(10,26),(11,27),(12,28),(13,29),(14,30),(15,31)]<br>
[(1,16),(2,8),(3,17),(5,10),(6,9),(7,28),(11,26),(12,20),(13,19),(14,21),(15,30),(18,24),(22,25),(23,29),(27,32)]<br>
[(3,12),(4,16),(5,18),(6,17),(7,11),(13,22),(14,27),(15,23),(19,25),(26,28),(29,30)]<br>
[(1,4),(3,5),(7,13),(9,18),(11,21),(12,24),(14,16),(15,27),(17,20),(19,26),(23,32),(25,28)]<br>
[(5,9),(7,16),(8,14),(10,17),(11,22),(15,19),(18,20),(21,26),(23,27),(31,32)]<br>
[(2,8),(6,9),(7,14),(10,12),(11,15),(13,16),(17,24),(19,23),(22,25),(27,29),(30,31)]<br>
[(1,2),(4,8),(6,7),(11,18),(12,14),(13,17),(15,20),(16,24),(19,21),(23,28),(26,27),(29,30)]<br>
[(0,1),(2,4),(3,6),(5,12),(7,10),(9,14),(11,13),(15,17),(16,18),(19,22),(20,24),(21,25),(23,26),(27,28)]<br>
[(3,4),(5,6),(7,8),(9,12),(10,11),(13,14),(15,16),(17,18),(19,20),(21,23),(22,24),(25,26),(28,29)]<br>
[(5,7),(6,8),(9,10),(11,12),(13,15),(14,16),(17,19),(18,20),(21,22),(23,24),(26,27)]<br>
[(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17),(18,19),(20,21),(22,23),(24,25)]<br>
</p></td><td>
Auto generated</td></tr>
<tr id="N34L209D17"><td>Sorting network for 34 inputs, 209 CEs, 17 layers:<br>
<p class="mono">[(0,33),(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16),(17,18),(19,20),(21,22),(23,24),(25,26),(27,28),(29,30),(31,32)]<br>
[(1,3),(2,4),(5,7),(6,8),(9,11),(10,12),(13,15),(14,16),(17,19),(18,20),(21,23),(22,24),(25,27),(26,28),(29,31),(30,32)]<br>
[(1,5),(2,6),(3,7),(4,8),(9,13),(10,14),(11,15),(12,16),(17,21),(18,22),(19,23),(20,24),(25,29),(26,30),(27,31),(28,32)]<br>
[(1,9),(2,10),(3,11),(4,12),(5,13),(6,14),(7,15),(8,16),(17,25),(18,26),(19,27),(20,28),(21,29),(22,30),(23,31),(24,32)]<br>
[(1,17),(2,18),(3,19),(4,20),(5,21),(6,22),(7,23),(8,24),(9,25),(10,26),(11,27),(12,28),(13,29),(14,30),(15,31),(16,32)]<br>
[(0,4),(2,3),(5,17),(6,11),(7,10),(8,12),(14,15),(16,28),(18,19),(21,25),(22,27),(23,26),(29,33),(30,31)]<br>
[(0,7),(2,9),(4,13),(8,14),(19,25),(20,29),(24,31),(26,33)]<br>
[(0,9),(4,18),(7,21),(8,19),(10,20),(12,26),(13,23),(14,25),(15,29),(24,33)]<br>
[(0,5),(3,7),(6,10),(9,17),(11,20),(12,15),(13,22),(16,24),(18,21),(23,27),(26,30),(28,33)]<br>
[(0,1),(3,5),(4,6),(7,17),(10,13),(11,18),(15,22),(16,26),(20,23),(27,29),(28,30),(32,33)]<br>
[(4,9),(6,11),(8,10),(12,15),(13,19),(14,20),(18,21),(22,27),(23,25),(24,29)]<br>
[(2,4),(5,9),(6,7),(11,17),(12,18),(13,14),(15,21),(16,22),(19,20),(24,28),(26,27),(29,31)]<br>
[(1,2),(3,4),(7,8),(10,17),(12,13),(14,18),(15,19),(16,23),(20,21),(25,26),(29,30),(31,32)]<br>
[(2,3),(4,5),(7,9),(8,11),(10,12),(13,17),(14,15),(16,20),(18,19),(21,23),(22,25),(24,26),(28,29),(30,31)]<br>
[(6,7),(8,9),(11,12),(13,14),(16,17),(19,20),(21,22),(24,25),(26,27)]<br>
[(5,6),(7,8),(10,11),(12,13),(15,16),(17,18),(20,21),(22,23),(25,26),(27,28)]<br>
[(9,10),(14,15),(16,17),(18,19),(23,24)]<br>
</p>Improved size over Batcher and Van Voorhis merges</td><td>
Auto generated</td></tr>
<tr id="N34L210D16"><td>Sorting network for 34 inputs, 210 CEs, 16 layers:<br>
<p class="mono">[(0,33),(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16),(17,18),(19,20),(21,22),(23,24),(25,26),(27,28),(29,30),(31,32)]<br>
[(1,3),(2,4),(5,7),(6,8),(9,11),(10,12),(13,15),(14,16),(17,19),(18,20),(21,23),(22,24),(25,27),(26,28),(29,31),(30,32)]<br>
[(1,5),(2,6),(3,7),(4,8),(9,13),(10,14),(11,15),(12,16),(17,21),(18,22),(19,23),(20,24),(25,29),(26,30),(27,31),(28,32)]<br>
[(1,9),(2,10),(3,11),(4,12),(5,13),(6,14),(7,15),(8,16),(17,25),(18,26),(19,27),(20,28),(21,29),(22,30),(23,31),(24,32)]<br>
[(0,20),(1,17),(2,3),(5,9),(6,10),(7,11),(8,12),(13,33),(14,15),(16,32),(18,19),(21,25),(22,26),(23,27),(24,28),(30,31)]<br>
[(0,17),(2,18),(3,19),(4,20),(5,21),(6,7),(8,24),(9,25),(10,11),(12,28),(13,29),(14,30),(15,31),(16,33),(22,23),(26,27)]<br>
[(0,1),(4,17),(6,22),(7,23),(8,19),(10,26),(11,27),(12,20),(13,21),(14,25),(16,29),(32,33)]<br>
[(1,6),(3,13),(4,18),(7,21),(8,14),(11,17),(12,26),(15,29),(16,22),(19,25),(20,30),(27,32)]<br>
[(1,2),(3,5),(4,9),(10,18),(11,16),(12,14),(15,23),(17,22),(19,21),(24,29),(28,30),(31,32)]<br>
[(1,3),(2,4),(7,10),(8,11),(9,13),(12,19),(14,21),(15,16),(17,18),(20,24),(22,25),(23,26),(29,31),(30,32)]<br>
[(2,3),(4,5),(6,11),(8,9),(10,13),(15,17),(16,18),(20,23),(22,27),(24,25),(28,29),(30,31)]<br>
[(3,4),(5,7),(6,10),(11,13),(12,15),(14,17),(16,19),(18,21),(20,22),(23,27),(26,28),(29,30)]<br>
[(6,8),(7,9),(11,12),(13,15),(14,16),(17,19),(18,20),(21,22),(24,26),(25,27)]<br>
[(5,6),(7,8),(9,10),(13,14),(15,17),(16,18),(19,20),(23,24),(25,26),(27,28)]<br>
[(4,5),(6,7),(9,11),(10,12),(15,16),(17,18),(21,23),(22,24),(26,27),(28,29)]<br>
[(8,9),(10,11),(12,13),(14,15),(16,17),(18,19),(20,21),(22,23),(24,25)]<br>
</p></td><td>
Auto generated</td></tr>
<tr id="N34L213D15"><td>Sorting network for 34 inputs, 213 CEs, 15 layers:<br>
<p class="mono">[(0,33),(1,2),(3,4),(5,6),(7,8),(9,10),(11,12),(13,14),(15,16),(17,18),(19,20),(21,22),(23,24),(25,26),(27,28),(29,30),(31,32)]<br>
[(1,3),(2,4),(5,7),(6,8),(9,11),(10,12),(13,15),(14,16),(17,19),(18,20),(21,23),(22,24),(25,27),(26,28),(29,31),(30,32)]<br>
[(1,5),(2,6),(3,7),(4,8),(9,13),(10,14),(11,15),(12,16),(17,21),(18,22),(19,23),(20,24),(25,29),(26,30),(27,31),(28,32)]<br>
[(1,9),(2,10),(3,11),(4,12),(5,13),(6,14),(7,15),(8,16),(17,25),(18,26),(19,27),(20,28),(21,29),(22,30),(23,31),(24,32)]<br>
[(1,17),(2,18),(3,19),(4,20),(5,21),(6,22),(7,23),(8,24),(9,25),(10,26),(11,27),(12,28),(13,29),(14,30),(15,31),(16,32)]<br>
[(0,1),(2,3),(4,13),(5,9),(6,11),(7,10),(8,12),(14,15),(18,19),(20,29),(21,25),(22,27),(23,26),(24,28),(30,31),(32,33)]<br>
[(1,22),(2,5),(3,9),(6,21),(7,18),(8,19),(10,13),(11,32),(12,27),(14,25),(15,26),(20,23),(24,30),(28,31)]<br>
[(1,9),(4,11),(8,14),(10,21),(12,23),(13,20),(15,17),(16,18),(19,25),(22,29),(24,32)]<br>
[(1,3),(4,15),(5,8),(9,13),(11,16),(17,22),(18,29),(20,24),(25,28),(30,32)]<br>
[(1,4),(3,7),(6,15),(8,11),(9,10),(12,17),(13,14),(16,21),(18,27),(19,20),(22,25),(23,24),(26,30),(29,32)]<br>
[(1,2),(3,6),(4,5),(7,15),(8,9),(10,11),(12,19),(13,16),(14,21),(17,20),(18,26),(22,23),(24,25),(27,30),(28,29),(31,32)]<br>
[(2,4),(6,10),(7,9),(11,15),(12,13),(14,17),(16,19),(18,22),(20,21),(23,27),(24,26),(29,31)]<br>
[(3,4),(5,7),(6,8),(9,10),(11,12),(13,15),(14,16),(17,19),(18,20),(21,22),(23,24),(25,27),(26,28),(29,30)]<br>
[(5,6),(7,8),(9,11),(10,12),(13,14),(15,16),(17,18),(19,20),(21,23),(22,24),(25,26),(27,28)]<br>
[(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17),(18,19),(20,21),(22,23),(24,25),(26,27),(28,29)]<br>
</p>Improved depth compared to Batcher O-E merge</td><td>
Auto generated</td></tr>
<tr id="N35L220D17"><td>Sorting network for 35 inputs, 220 CEs, 17 layers:<br>
<p class="mono">[(0,1),(2,3),(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17),(18,19),(20,21),(22,23),(24,25),(26,27),(28,29),(30,31),(32,33)]<br>
[(0,2),(1,3),(4,6),(5,7),(8,10),(9,11),(12,14),(13,15),(16,18),(17,19),(20,22),(21,23),(24,26),(25,27),(28,30),(29,31),(33,34)]<br>
[(0,4),(1,5),(2,6),(3,7),(8,12),(9,13),(10,14),(11,15),(16,20),(17,21),(18,22),(19,23),(24,28),(25,29),(26,30),(27,31),(32,33)]<br>
[(0,8),(1,9),(2,10),(3,11),(4,12),(5,13),(6,14),(7,15),(16,24),(17,25),(18,26),(19,27),(20,28),(21,29),(22,30),(23,31)]<br>
[(0,16),(1,17),(2,18),(3,19),(4,20),(5,21),(6,22),(7,23),(8,24),(9,25),(10,26),(11,27),(12,28),(13,29),(14,30),(15,31)]<br>
[(0,32),(1,2),(3,12),(4,8),(5,10),(6,9),(7,11),(13,14),(17,18),(19,28),(20,24),(21,26),(22,25),(23,27),(29,30),(31,34)]<br>
[(5,6),(9,19),(14,28),(15,31),(16,32),(17,33),(18,24),(21,22)]<br>
[(1,17),(3,16),(9,21),(10,32),(13,33),(14,22),(15,20),(19,26),(30,31)]<br>
[(1,3),(2,15),(7,13),(8,17),(10,16),(11,33),(20,32),(23,30)]<br>
[(3,4),(5,16),(6,17),(7,15),(11,19),(12,20),(13,24),(23,29),(25,32),(26,33)]<br>
[(1,3),(4,8),(5,10),(6,7),(9,12),(13,15),(14,25),(16,18),(19,24),(20,21),(28,32),(29,33)]<br>
[(2,5),(10,16),(11,20),(12,14),(17,18),(21,23),(22,25),(26,28),(27,33),(30,32)]<br>
[(2,4),(5,8),(9,16),(11,17),(12,13),(14,15),(18,20),(19,26),(21,22),(23,25),(24,28),(27,30),(31,33)]<br>
[(2,3),(4,5),(6,9),(7,16),(8,10),(11,12),(13,18),(14,17),(15,20),(19,21),(22,24),(23,26),(25,28),(27,29),(31,32)]<br>
[(6,8),(7,9),(10,11),(12,14),(13,16),(15,19),(17,18),(20,21),(22,23),(24,26),(25,27),(28,29),(30,31)]<br>
[(5,6),(7,10),(9,11),(12,13),(14,16),(15,17),(18,19),(20,22),(21,23),(24,25),(26,27),(29,30)]<br>
[(7,8),(9,10),(11,12),(13,14),(15,16),(17,18),(19,20),(21,22),(23,24),(25,26),(27,28)]<br>
</p>Improved size over Batcher and Van Voorhis merges</td><td>
Auto generated</td></tr>
<tr id="N35L221D16"><td>Sorting network for 35 inputs, 221 CEs, 16 layers:<br>
<p class="mono">[(0,1),(2,3),(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17),(18,19),(20,21),(22,23),(24,25),(26,27),(28,29),(30,31),(32,33)]<br>
[(0,2),(1,3),(4,6),(5,7),(8,10),(9,11),(12,14),(13,15),(16,18),(17,19),(20,22),(21,23),(24,26),(25,27),(28,30),(29,31),(33,34)]<br>
[(0,4),(1,5),(2,6),(3,7),(8,12),(9,13),(10,14),(11,15),(16,20),(17,21),(18,22),(19,23),(24,28),(25,29),(26,30),(27,31),(32,33)]<br>
[(0,8),(1,9),(2,10),(3,11),(4,12),(5,13),(6,14),(7,15),(16,24),(17,25),(18,26),(19,27),(20,28),(21,29),(22,30),(23,31)]<br>
[(0,16),(1,17),(2,18),(3,19),(4,20),(5,21),(6,22),(7,23),(8,24),(9,25),(10,26),(11,27),(12,28),(13,29),(14,30),(15,31)]<br>
[(1,2),(3,12),(4,8),(5,10),(6,9),(7,11),(13,14),(15,34),(16,32),(17,18),(19,28),(20,24),(21,26),(22,25),(23,27),(29,30)]<br>
[(0,16),(5,6),(9,19),(10,32),(15,20),(17,33),(18,24),(21,22),(23,29),(25,28),(27,30),(31,34)]<br>
[(1,17),(2,15),(3,10),(4,16),(7,33),(9,32),(12,20),(19,26),(23,25),(28,31)]<br>
[(1,4),(3,16),(5,10),(6,15),(7,13),(8,17),(11,20),(12,21),(14,33),(22,23)]<br>
[(3,4),(5,16),(7,18),(9,12),(10,17),(11,22),(13,19),(14,24),(20,26),(21,32),(23,33)]<br>
[(2,5),(4,8),(6,7),(9,10),(11,14),(12,17),(13,21),(15,18),(19,24),(20,28),(22,32),(26,29),(27,33)]<br>
[(2,4),(5,8),(6,9),(7,16),(11,12),(13,15),(14,17),(18,21),(19,23),(20,22),(24,32),(25,28),(26,27),(31,33)]<br>
[(2,3),(4,5),(7,8),(10,16),(11,13),(12,15),(14,18),(17,21),(19,20),(22,23),(24,25),(28,32),(29,31),(30,33)]<br>
[(6,7),(8,9),(10,11),(12,14),(13,16),(15,17),(18,19),(20,24),(21,22),(23,26),(25,28),(29,32)]<br>
[(5,6),(8,10),(9,11),(12,13),(14,16),(15,18),(17,19),(20,21),(22,24),(23,25),(26,28),(27,29),(30,32)]<br>
[(7,8),(9,10),(11,12),(13,14),(15,16),(17,18),(19,20),(21,22),(23,24),(25,26),(27,28),(29,30),(31,32)]<br>
</p></td><td>
Auto generated</td></tr>
<tr id="N36L227D18"><td>Sorting network for 36 inputs, 227 CEs, 18 layers:<br>
<p class="mono">[(0,1),(2,3),(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17),(18,19),(20,21),(22,23),(24,25),(26,27),(28,29),(30,31),(32,33),(34,35)]<br>
[(0,34),(1,35),(2,4),(3,5),(6,8),(7,9),(10,12),(11,13),(14,16),(15,17),(18,20),(19,21),(22,24),(23,25),(26,28),(27,29),(30,32),(31,33)]<br>
[(2,6),(3,7),(4,8),(5,9),(10,14),(11,15),(12,16),(13,17),(18,22),(19,23),(20,24),(21,25),(26,30),(27,31),(28,32),(29,33)]<br>
[(2,10),(3,11),(4,12),(5,13),(6,14),(7,15),(8,16),(9,17),(18,26),(19,27),(20,28),(21,29),(22,30),(23,31),(24,32),(25,33)]<br>
[(2,18),(3,19),(4,20),(5,21),(6,22),(7,23),(8,24),(9,25),(10,26),(11,27),(12,28),(13,29),(14,30),(15,31),(16,32),(17,33)]<br>
[(0,2),(1,3),(4,10),(5,11),(8,26),(9,27),(12,22),(13,23),(14,20),(15,21),(24,30),(25,31),(32,34),(33,35)]<br>
[(1,10),(2,12),(3,22),(11,19),(13,32),(16,24),(23,33),(25,34)]<br>
[(2,18),(3,12),(7,13),(17,33),(22,28),(23,32)]<br>
[(3,8),(5,23),(6,18),(7,11),(12,30),(13,19),(16,22),(17,29),(24,28),(27,32)]<br>
[(1,6),(4,7),(5,14),(8,20),(9,23),(10,18),(11,13),(12,26),(15,27),(17,25),(21,30),(22,24),(28,31),(29,34)]<br>
[(2,4),(3,5),(7,8),(9,15),(12,14),(20,26),(21,23),(27,28),(30,32),(31,33)]<br>
[(1,2),(4,6),(7,10),(8,18),(9,22),(11,20),(13,26),(14,16),(15,24),(17,27),(19,21),(25,28),(29,31),(33,34)]<br>
[(2,4),(3,7),(5,8),(9,14),(11,12),(13,18),(15,16),(17,22),(19,20),(21,26),(23,24),(27,30),(28,32),(31,33)]<br>
[(3,4),(5,11),(6,7),(8,12),(9,13),(14,18),(15,19),(16,20),(17,21),(22,26),(23,27),(24,30),(28,29),(31,32)]<br>
[(4,6),(7,10),(9,11),(12,15),(13,14),(16,17),(18,19),(20,23),(21,22),(24,26),(25,28),(29,31)]<br>
[(5,7),(8,10),(12,13),(14,15),(16,18),(17,19),(20,21),(22,23),(25,27),(28,30)]<br>
[(5,6),(8,9),(10,11),(13,14),(15,16),(17,18),(19,20),(21,22),(24,25),(26,27),(29,30)]<br>
[(7,8),(9,10),(11,12),(23,24),(25,26),(27,28)]<br>
</p>Improved size over Batcher and Van Voorhis merges</td><td>
Auto generated</td></tr>
<tr id="N36L228D17"><td>Sorting network for 36 inputs, 228 CEs, 17 layers:<br>
<p class="mono">[(0,1),(2,3),(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17),(18,19),(20,21),(22,23),(24,25),(26,27),(28,29),(30,31),(32,33),(34,35)]<br>
[(0,34),(1,35),(2,4),(3,5),(6,8),(7,9),(10,12),(11,13),(14,16),(15,17),(18,20),(19,21),(22,24),(23,25),(26,28),(27,29),(30,32),(31,33)]<br>
[(1,34),(2,6),(3,7),(4,8),(5,9),(10,14),(11,15),(12,16),(13,17),(18,22),(19,23),(20,24),(21,25),(26,30),(27,31),(28,32),(29,33)]<br>
[(2,10),(3,11),(4,12),(5,13),(6,14),(7,15),(8,16),(9,17),(18,26),(19,27),(20,28),(21,29),(22,30),(23,31),(24,32),(25,33)]<br>
[(2,18),(3,19),(4,20),(5,21),(6,22),(7,23),(8,24),(9,25),(10,26),(11,27),(12,28),(13,29),(14,30),(15,31),(16,32),(17,33)]<br>
[(0,2),(3,4),(5,26),(6,10),(7,8),(9,30),(11,20),(12,19),(15,24),(16,23),(25,29),(27,28),(31,32),(33,35)]<br>
[(1,7),(2,18),(11,12),(15,16),(17,33),(19,20),(23,24),(28,34)]<br>
[(1,5),(2,6),(7,21),(8,20),(9,17),(14,28),(15,27),(18,26),(29,33),(30,34)]<br>
[(7,9),(10,18),(13,21),(14,22),(17,25),(26,28)]<br>
[(4,14),(5,7),(6,10),(9,13),(12,18),(17,23),(21,31),(22,26),(25,29),(28,30)]<br>
[(1,10),(4,6),(5,11),(7,19),(8,22),(9,15),(13,27),(14,18),(16,28),(17,21),(20,26),(24,30),(25,34),(29,31)]<br>
[(1,3),(7,9),(8,14),(10,12),(13,15),(16,18),(17,19),(20,22),(21,27),(23,25),(26,28),(32,34)]<br>
[(1,2),(3,6),(5,10),(7,12),(9,11),(13,18),(15,19),(16,20),(17,22),(23,28),(24,26),(25,30),(29,32),(33,34)]<br>
[(2,4),(3,5),(6,7),(8,10),(9,16),(11,20),(12,14),(13,17),(15,24),(18,22),(19,26),(21,23),(25,27),(28,29),(30,32),(31,33)]<br>
[(3,4),(5,6),(7,12),(9,10),(11,13),(14,16),(15,17),(18,20),(19,21),(22,24),(23,28),(25,26),(29,30),(31,32)]<br>
[(6,8),(7,9),(10,12),(11,14),(13,16),(15,18),(17,20),(19,22),(21,24),(23,25),(26,28),(27,29)]<br>
[(5,6),(7,8),(9,10),(11,12),(13,14),(15,16),(17,18),(19,20),(21,22),(23,24),(25,26),(27,28),(29,30)]<br>
</p></td><td>
Auto generated</td></tr>
<tr id="N36L229D16"><td>Sorting network for 36 inputs, 229 CEs, 16 layers:<br>
<p class="mono">[(0,1),(2,3),(4,5),(6,7),(8,9),(10,11),(12,13),(14,15),(16,17),(18,19),(20,21),(22,23),(24,25),(26,27),(28,29),(30,31),(32,33),(34,35)]<br>
[(0,2),(1,3),(4,6),(5,7),(8,10),(9,11),(12,14),(13,15),(16,18),(17,19),(20,22),(21,23),(24,26),(25,27),(28,30),(29,31),(32,34),(33,35)]<br>
[(0,4),(1,5),(2,6),(3,7),(8,12),(9,13),(10,14),(11,15),(20,24),(21,25),(22,26),(23,27),(28,32),(29,33),(30,34),(31,35)]<br>
[(0,8),(1,9),(2,10),(3,11),(4,12),(5,13),(6,14),(7,15),(20,28),(21,29),(22,30),(23,31),(24,32),(25,33),(26,34),(27,35)]<br>
[(0,20),(1,21),(2,22),(3,23),(4,24),(5,25),(6,26),(7,27),(8,28),(9,29),(10,30),(11,31),(12,32),(13,33),(14,34),(15,35)]<br>
[(2,8),(3,28),(4,16),(5,17),(6,12),(7,32),(9,22),(10,21),(13,26),(14,25),(18,30),(19,31),(23,29),(27,33)]<br>
[(3,18),(5,24),(7,19),(8,20),(9,10),(11,30),(13,14),(15,27),(16,28),(17,32),(21,22),(25,26)]<br>
[(1,5),(2,3),(4,8),(6,21),(7,18),(12,22),(13,23),(14,29),(15,19),(16,20),(17,28),(27,31),(30,34),(32,33)]<br>