The Spectrum of Self-converse \(MTS\)

A Mendelsohn triple system, \(MTS(v) = (X, \mathcal{B})\), is called self-converse if it and its converse \((X, \mathcal{B}^{-1})\) are isomorphic, where \(\mathcal{B}^{-1 } = \{\langle z,y,x\rangle; \langle x,y,z\rangle \in \mathcal{B}\}\). In this paper, the existence spectrum of self-converse \(MTS(v)\) is given, which is \(v \equiv 0\) or \(1 \pmod{3}\) and \(v \neq 6\).