Enumeration of MOLS of small order

Judith Egan, Ian M Wanless

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We report the results of a computer investigation of sets of mutually orthogonal Latin squares (MOLS) of small order. For n ≤ 9 we: (1) determine the number of orthogonal mates for each species of Latinsquare 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; (3) classify all sets of MOLS of order n 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.
Original languageEnglish
Pages (from-to)799-824
Number of pages26
JournalMathematics of Computation
Issue number298
Publication statusPublished - 2016


  • Latin square
  • MOLS
  • transversal
  • plex
  • orthogonal mate

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