### Abstract

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 language | English |
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Pages (from-to) | 799-824 |

Number of pages | 26 |

Journal | Mathematics of Computation |

Volume | 85 |

Issue number | 298 |

DOIs | |

Publication status | Published - 2016 |

### Keywords

- Latin square
- MOLS
- transversal
- plex
- orthogonal mate

## Cite this

Egan, J., & Wanless, I. M. (2016). Enumeration of MOLS of small order.

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