Bounds on the maximum number of Latin squares in a mutually quasi-orthogonal set

AbstractIn this paper we are concerned with finding an upper bound on Nq(n), the maximum number of Latin squares of order n in a mutually quasi-orthogonal set. In doing so, we make use of relationships with orthogonal frequency squares, equidistant permutation arrays and Room squares. We improve upon the best-known bound for Nq(n), n⩾8, by showing that Nq(n)⩽R(n), where R(n) is the maximum number of rows in an equidistant permutation array with n columns and index 1. Much improved bounds are found for special cases