Document Zbl 1332.05025

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Comput.</a> <a href="/?q=in%3A353422" title="Articles in this Issue">85, No. 298, 799-824 (2016)</a>. </div> <div class="abstract">Summary: We report the results of a computer investigation of sets of mutually orthogonal Latin squares (MOLS) of small order. For $ n\leq 9$ we: (1) determine the number of orthogonal mates for each species of Latin square of order $ n$, (2) calculate the proportion of Latin squares of order $ n$ that have an orthogonal mate, and the expected number of mates when a square is chosen uniformly at random, and (3) classify all sets of MOLS of order $ n$ up to various different notions of equivalence.<br class="zbmathjax-paragraph"> We also provide a triple of Latin squares of order 10 that is the closest to being a set of MOLS so far found.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6552496">Cited in <strong>25</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A05B15" title="MSC2020">05B15</a> </td> <td class="space"> Orthogonal arrays, Latin squares, Room squares </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A05D15" title="MSC2020">05D15</a> </td> <td class="space"> Transversal (matching) theory </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A62K99" title="MSC2020">62K99</a> </td> <td class="space"> Design of statistical experiments </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3ALatin+square">Latin square</a>; <a href="/?q=ut%3AMOLS">MOLS</a>; <a href="/?q=ut%3Atransversal">transversal</a>; <a href="/?q=ut%3Aplex">plex</a>; <a href="/?q=ut%3Aorthogonal+mate">orthogonal mate</a></div> <div class="software"> <h3>Software:</h3><a href="/software/611">nauty</a>; <a href="/software/7823">Traces</a>; <a href="/software/17197">libexact</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1332.05025" data-ciurl="/ci/06552496" data-biburl="/bibtex/06552496.bib" data-amsurl="/amsrefs/06552496.bib" data-xmlurl="/xml/06552496.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06552496.pdf" title="Zbl 1332.05025 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1090/mcom/3010" aria-label="DOI for “Enumeration of MOLS of small order”" title="10.1090/mcom/3010">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/1406.3681"title="Note: arXiv document may differ from published version">arXiv</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">[Bose1938] R. 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