Large sets of disjoint pure Mendelsohn triple systems (Q5935430)

A pair \((X,{\mathcal B})\) is called a Mendelson triple system of order \(v\), briefly \(\text{MTS}(v)\), if \(|X|= v\) and \({\mathcal B}\) is a collection of cyclic triples \(\langle x,y,z\rangle= \{(x,y), (y,z),(z,x)\}\) on \(X\) such that every ordered pair of elements in \(X\) belongs to exactly one triple of \({\mathcal B}\). If \(\langle x,y,z\rangle\in{\mathcal B}\) implies \(\langle z,y,x\rangle\not\in{\mathcal B}\), then the MTS is called pure and is denoted by \(\text{PMTS}(v)\). The authors give some preliminary results on the existence and non-existence of large sets and overlarge sets in a \(\text{PMTS}(v)\).