Pairs of MOLS of order ten satisfying non-trivial relations

DOI10.1007/S10623-022-01149-6arXiv2204.10996MaRDI QIDQ6397260

Michael J. Gill, Ian M. Wanless

Publication date: 23 April 2022

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.

Mathematics Subject Classification ID

Orthogonal arrays, Latin squares, Room squares (05B15) Finite partial geometries (general), nets, partial spreads (51E14)

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