The enumeration of cyclic mutually nearly orthogonal Latin squares

Research output: Contribution to journalArticleScientificpeer-review


  • Fatih Demirkale
  • Diane M. Donovan
  • Janne I. Kokkala
  • Trent G. Marbach

Research units

  • Yildiz Technical University
  • University of Queensland
  • Monash University


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.


Original languageEnglish
Pages (from-to)265-276
Number of pages12
JournalJournal of Combinatorial Designs
Issue number5
Early online date1 Jan 2019
Publication statusPublished - 1 May 2019
MoE publication typeA1 Journal article-refereed

    Research areas

  • latin square, MNOLS, nearly orthogonal, NUMBER

ID: 32216845