A New Product Construction for Large Sets Of Resolvable Mendelsohn Triple Systems

Abstract

A large set of resolvable Mendelsohn triple systems of order \(v\), denoted by \(\text{LRMTS}(v)\), is a collection of \(v-2\) \(\text{RMTS}(v)\)s based on \(v\)-set \(X\), such that every Mendelsohn triple of \(X\) occurs as a block in exactly one of the \(v-2\) \(\text{RMTS}(v)\)s. In this paper, we use \(\text{TRIQ}\) and \(\text{LR-design}\) to present a new product construction for \(\text{LRMTS}(v)\)s. This provides some new infinite families of \(\text{LRMTS}(v)\)s.