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In this paper, we study collections of mutually nearly orthogonal Latin squares (MNOLS), which come from a modification of the orthogonality condition for mutually orthogonal Latin squares. In particular, we… Click to show full abstract
In this paper, we study collections of mutually nearly orthogonal Latin squares (MNOLS), which come from a modification of the orthogonality condition for mutually orthogonal Latin squares. In particular, we find the maximum μ such that there exists a set of μ cyclic MNOLS of order n for n≤18, as well as providing a full enumeration of sets and lists of μ cyclic MNOLS of order n under a variety of equivalences with n≤18. This resolves in the negative a conjecture that proposed that the maximum μ for which a set of μ cyclic MNOLS of order n exists is [n/4]+1.
Journal Title: Journal of Combinatorial Designs
Year Published: 2019
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