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arXiv · 1401.1466

A three-factor product construction for mutually orthogonal latin squares

Peter J. Dukes·Alan C. H. Ling
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Abstract

It is well known that mutually orthogonal latin squares, or MOLS, admit a (Kronecker) product construction. We show that, under mild conditions, `triple products' of MOLS can result in a gain of one square. In terms of transversal designs, the technique is to use a construction of Rolf Rees twice: once to obtain a coarse resolution of the blocks after one product, and next to reorganize classes and resolve the blocks of the second product. As consequences, we report a few improvements to the MOLS table and obtain a slight strengthening of the famous theorem of MacNeish.

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Peter J. Dukes, Alan C. H. Ling. 2014-01-07. A three-factor product construction for mutually orthogonal latin squares. https://arxiv.org/abs/1401.1466

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