Self-converse large sets of pure Mendelsohn triple systems

A Mendelsohn triple system of order . (MTS(.)) is a pair (X, .) where X is a .-set and . is a collection of cyclic triples on X such that every ordered pair of X belongs to exactly one triple of .. An MTS(.) (X, .) is called pure and denoted by PMTS(.) if .x, y, z. . . implies .z, y, x. . .. A large set of MTS(.)s (LMTS(.)) is a collection of . . 2 pairwise disjoint MTS(.)s on a .-set. A self-converse large set of PMTS(.)s, denoted by LPMTS*(.), is an LMTS(.) containing ...2/2. converse pairs of PMTS(.)s. In this paper, some results about the existence and non-existence for LPMTS*(.) are obtained.