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arXiv · 1512.00997

The Enumeration of Cyclic MNOLS

F. Demirkale·D. M. Donovan·J. I. Kokkala·T. G. Marbach
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Abstract

In this paper we study collections of mutually nearly orthogonal Latin squares ($\text{MNOLS}$), which come from a modification of the orthogonal condition for mutually orthogonal Latin squares. In particular, we find the maximum $\mu$ such that there exists a set of $\mu$ cyclic $\text{MNOLS}$ of order $n$ for $n \leq 18$, as well as providing a full enumeration of sets and lists of $\mu$ cyclic $\text{MNOLS}$ of order $n$ under a variety of equivalences with $n \leq 18$. This resolves in the negative a conjecture that proposed the maximum $\mu$ for which a set of $\mu$ cyclic $\text{MNOLS}$ of order $n$ exists is $\lceil n/4\rceil +1$.

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F. Demirkale, D. M. Donovan, J. I. Kokkala, T. G. Marbach. 2015-12-03. The Enumeration of Cyclic MNOLS. https://arxiv.org/abs/1512.00997

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