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A Three‐Factor Product Construction for Mutually Orthogonal Latin Squares
Author(s) -
Dukes Peter J.,
Ling Alan C.H.
Publication year - 2015
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.21393
Subject(s) - kronecker product , mathematics , transversal (combinatorics) , product (mathematics) , latin square , orthogonal array , combinatorics , table (database) , resolution (logic) , square (algebra) , kronecker delta , algebra over a field , pure mathematics , statistics , computer science , geometry , mathematical analysis , rumen , physics , food science , chemistry , quantum mechanics , artificial intelligence , taguchi methods , fermentation , data mining
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.