A three-factor product construction for mutually orthogonal latin squares
Combinatorics
2014-01-08 v1
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.
Keywords
Cite
@article{arxiv.1401.1466,
title = {A three-factor product construction for mutually orthogonal latin squares},
author = {Peter J. Dukes and Alan C. H. Ling},
journal= {arXiv preprint arXiv:1401.1466},
year = {2014}
}