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.