# Difference Covering Arrays and Pseudo-Orthogonal Latin Squares

Demirkale, Fatih, Donovan, Diane, Hall, Joanne, Khodkar, Abdollah and Rao, Asha (2015) Difference Covering Arrays and Pseudo-Orthogonal Latin Squares. Graphs and Combinatorics, 32 4: 1-22. doi:10.1007/s00373-015-1649-8

Author Demirkale, FatihDonovan, DianeHall, JoanneKhodkar, AbdollahRao, Asha Difference Covering Arrays and Pseudo-Orthogonal Latin Squares Graphs and Combinatorics   Check publisher's open access policy 0911-01191435-5914 2015-11-30 2015 Article (original research) 10.1007/s00373-015-1649-8 Not yet assessed 32 4 1 22 22 Tokyo, Japan Springer eng 2614 Theoretical Computer Science2607 Discrete Mathematics and Combinatorics A pair of Latin squares, A and B, of order n, is said to be pseudo-orthogonal if each symbol in A is paired with every symbol in B precisely once, except for one symbol with which it is paired twice and one symbol with which it is not paired at all. A set of t Latin squares, of order n, are said to be mutually pseudo-orthogonal if they are pairwise pseudo-orthogonal. A special class of pseudo-orthogonal Latin squares are the mutually nearly orthogonal Latin squares (MNOLS) first discussed in 2002, with general constructions given in 2007. In this paper we develop row complete MNOLS from difference covering arrays. We will use this connection to settle the spectrum question for sets of 3 mutually pseudo-orthogonal Latin squares of even order, for all but the order 146. A pair of Latin squares, A and B, of order n, is said to be pseudo-orthogonal if each symbol in A is paired with every symbol in B precisely once, except for one symbol with which it is paired twice and one symbol with which it is not paired at all. A set of t Latin squares, of order n, are said to be mutually pseudo-orthogonal if they are pairwise pseudo-orthogonal. A special class of pseudo-orthogonal Latin squares are the mutually nearly orthogonal Latin squares (MNOLS) first discussed in 2002, with general constructions given in 2007. In this paper we develop row complete MNOLS from difference covering arrays. We will use this connection to settle the spectrum question for sets of 3 mutually pseudo-orthogonal Latin squares of even order, for all but the order 146. Difference covering arrayLatin squaresPseudo-orthogonal Latin squaresMutually nearly orthogonal Latin squares C1 Provisional Code UQ

 Document type: Journal Article Article (original research) School of Mathematics and Physics Official 2016 Collection

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