A Three‐Factor Product Construction for Mutually Orthogonal Latin Squares |
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| Authors: | Peter J Dukes Alan CH Ling |
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| Affiliation: | 1. Mathematics and Statistics, University of Victoria, Victoria, CanadaResearch of Peter Dukes is supported by NSERC grant number 312595‐2010.;2. Computer Science, University of Vermont, Burlington, VT, USA |
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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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| Keywords: | orthogonal latin square transversal design direct product |
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