### Abstract

Original language | English |
---|---|

Pages (from-to) | 799-824 |

Number of pages | 26 |

Journal | Mathematics of Computation |

Volume | 85 |

Issue number | 298 |

DOIs | |

Publication status | Published - 2016 |

Externally published | Yes |

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### Cite this

*Mathematics of Computation*,

*85*(298), 799-824. https://doi.org/10.1090/mcom/3010

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*Mathematics of Computation*, vol. 85, no. 298, pp. 799-824. https://doi.org/10.1090/mcom/3010

**Enumeration of MOLS of small order.** / Egan, J.; Wanless, I.M.

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

T1 - Enumeration of MOLS of small order

AU - Egan, J.

AU - Wanless, I.M.

PY - 2016

Y1 - 2016

N2 - 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 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; (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. © 2015 American Mathematical Society.

AB - 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 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; (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. © 2015 American Mathematical Society.

KW - Latin square

KW - MOLS

KW - Orthogonal mate

KW - Plex

KW - Transversal

UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85000742203&doi=10.1090%2fmcom%2f3010&partnerID=40&md5=7f809f2518b4ba7a81547cc1770009fb

U2 - 10.1090/mcom/3010

DO - 10.1090/mcom/3010

M3 - Article

VL - 85

SP - 799

EP - 824

JO - Mathematics of Computation

JF - Mathematics of Computation

SN - 0025-5718

IS - 298

ER -