Enumeration of MOLS of small order

We report the results of a computer investigation of sets of mutually orthogonal Latin squares (MOLS) of small order. For n⩽9n\leqslant 9 we: determine the number of orthogonal mates for each species of Latin square of order nn; calculate the proportion of Latin squares of order nn that have an orth...

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Bibliographic Details
Published in:Mathematics of computation 2016-03, Vol.85 (298), p.799-824
Main Authors: Egan, Judith, Wanless, Ian M.
Format: Article
Language:English
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Research article
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Summary:We report the results of a computer investigation of sets of mutually orthogonal Latin squares (MOLS) of small order. For n⩽9n\leqslant 9 we: determine the number of orthogonal mates for each species of Latin square of order nn; calculate the proportion of Latin squares of order nn that have an orthogonal mate, and the expected number of mates when a square is chosen uniformly at random; classify all sets of MOLS of order nn up to various different notions of equivalence. We also provide a triple of Latin squares of order 10 that is the closest to being a set of MOLS so far found.
ISSN:0025-5718
1088-6842
DOI:10.1090/mcom/3010