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The enumeration of cyclic mutually nearly orthogonal Latin squares

Journal of Combinatorial Designs, ISSN: 1520-6610, Vol: 27, Issue: 5, Page: 265-276
2019
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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 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.

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