Difference Covering Arrays and Pseudo-Orthogonal Latin Squares

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.