Frame self-orthogonal Mendelsohn triple systems of type \(h^n\). (English) Zbl 1157.05012
Summary: A Mendelsohn triple system (MTS) corresponds to an idempotent semisymmetric Latin square (quasigroup) of the same order. A holey MTS is called frame self-orthogonal, briefly FSOMTS, if its associated holey semisymmetric Latin square is frame self-orthogonal. In this paper, we use FSOMTS\((h^n)\) to denote an FSOMTS with \(n\) spanning holes of size \(h\). The existence of FSOMTS\((h^n)\) for \(h\leqslant 3\) has been known with a few exceptions. We extend the existing results and determine the necessary and sufficient conditions for the existence of FSOMTS\((h^n)\) for any \(h\) and \(n\) with some possible exceptions.
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