On Directed Incomplete Transversal Designs with Block Size Five

Abstract

Let $v$ and $u$ be positive integers. It is shown in this paper that the necessary condition for the existence of a directed $\mathrm{T}\mathrm{D}(5,v)$-$\mathrm{T}\mathrm{D}(5,u)$, namely $v\ge 4u$, is also sufficient.