Difference Covering Arrays and Pseudo-Orthogonal Latin Squares

TL;DR

This paper explores the connection between difference covering arrays and pseudo-orthogonal Latin squares, specifically constructing mutually nearly orthogonal Latin squares and resolving a spectrum question for certain orders.

Contribution

It introduces a method to develop row complete MNOLS from difference covering arrays and addresses the spectrum question for three mutually pseudo-orthogonal Latin squares of even order.

Findings

Constructed row complete MNOLS from difference covering arrays.

Resolved the spectrum question for 3 mutually pseudo-orthogonal Latin squares of even order, except 146.

Provided general constructions for MNOLS.

Abstract

Difference arrays are used in applications such as software testing, authentication codes and data compression. Pseudo-orthogonal Latin squares are used in experimental designs. 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.