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Encyclopaedia of DesignTheory: MOLS

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MOLS as partitions

A set of s MOLS of order n can be represented by a set of n2 cells together with s+2 partitions of the set of cells into n sets of size n, any two of the partitions being orthogonal.

For the first two partitions give the set of cells the structure of a square grid or array, and each subsequent partition then defines a Latin square; the orthogonality of the partitions then translates into the orthogonality of the squares.


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Peter J. Cameron
16 April 2002