On the Existence of Perfect Mendelsohn Designs without Repeated Blocks

Abstract

In this paper we study the existence of perfect Mendelsohn designs without repeated blocks and give several general constructions. We prove that for $k=3$ and any $\lambda$, and $(k,\lambda )=(4,2),(4,3)$ and $(4,4)$, the necessary conditions are also sufficient for the existence of a simple $(v,k,\lambda )$-PMD, with the exceptions $(k,\lambda )=(6,1)$ and $(6,3)$.