Pairs of MOLS of order ten satisfying non-trivial relations
A relation on a k net(n) (or, equivalently, a set of k-2 mutually
orthogonal Latin squares of order n) is an F2 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 18526320 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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