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On the existence of MOLS with equal-sized holes

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Abstract

We consider a pair of MOLS (mutually orthogonal Latin squares) having holes, corresponding to missing sub-MOLS, which are disjoint and spanning It is shown that a pair of MOLS withn holes of sizeh exist forh ≥ 2 if and only ifn ≥ 4 For SOLS (self-orthogonal Latin squares) with holes, we have the same result, with two possible exceptions SOLS with 7 or 13 holes of size 6

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Authors and Affiliations

  1. Department of Computer Science, University of Manitoba, R3T 2N2, Winnipeg, Manitoba, Canada

    D R. Stinson & L Zhu

  2. Department of Mathematics, Suzhou University, People's Republic of China

    D R. Stinson & L Zhu

Authors
  1. D R. Stinson
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  2. L Zhu
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Stinson, D.R., Zhu, L. On the existence of MOLS with equal-sized holes. Aeq. Math. 33, 96–105 (1987). https://doi.org/10.1007/BF01836155

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  • DOI: https://doi.org/10.1007/BF01836155

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