Abstract
We improve the existence results for holey self-orthogonal Latin squares with symmetric orthogonal mates (HSOLSSOMs) and show that the necessary conditions for the existence of a HSOLSSOM of typeh n are also sufficient with at most 28 pairs (h, n) of possible exceptions.
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Research supported in part by NSERC Grant A-5320 for the first author, NSF Grants CCR-9504205 and CCR-9357851 for the second author, and NSFC Grant 19231060-2 for the third author.
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Bennett, F.E., Zhang, H. & Zhu, L. Holey self-orthogonal Latin squares with symmetric orthogonal mates. Annals of Combinatorics 1, 107–118 (1997). https://doi.org/10.1007/BF02558468
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DOI: https://doi.org/10.1007/BF02558468