The search for a triple of mutually orthogonal Latin squares of order ten: looking through pairs of dimension thirty-five and less

Date

2010-08-24T20:19:13Z

Authors

Delisle, Erin

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Abstract

A computer generation of all pairs of mutually orthogonal Latin squares of order ten and dimension 35 or less is undertaken. All such pairs are successfully generated up to main class equivalence. No pairs of mutually orthogonal Latin squares of order ten exist for dimension 33. Six dimension 34 pairs, which are counterexamples to a conjecture by Moorehouse, are found. Eighty-five pairs can be formed with dimension 35. None of the pairs can be extended to a triple. If a triple of mutually orthogonal Latin squares exists for order ten, the pairs of Latin squares in the triple must be of dimension 36 or 37.

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Keywords

mutually orthogonal Latin squares, backtracking

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