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arXiv · 2204.10996

Pairs of MOLS of order ten satisfying non-trivial relations

Michael J. Gill·Ian M. Wanless
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Abstract

A relation on a $k$-net$(n)$ (or, equivalently, a set of $k-2$ mutually orthogonal Latin squares of order $n$) is an $\mathbb{F}_{2}$ linear dependence within the incidence matrix of the net. Dukes and Howard (2014) showed that any 6-net(10) satisfies at least two non-trivial relations, and classified the relations that could appear in such a net. We find that, up to equivalence, there are $18\,526\,320$ pairs of MOLS satisfying at least one non-trivial relation. None of these pairs extend to a triple. We also rule out one other relation on a set of $3$-MOLS from Dukes and Howard's classification.

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Michael J. Gill, Ian M. Wanless. 2022-04-23. Pairs of MOLS of order ten satisfying non-trivial relations. https://doi.org/10.1007/s10623-022-01149-6

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