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 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.
| 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
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