Perfect Mendelsohn Designs With Equal-Sized Holes

Abstract

It is shown that the obvious necessary condition $\lambda h(h–1)m^2\equiv 0(\mathrm{mod}k)$ for the existence of a $(v,k,\lambda )$-perfect Mendelsohn design with $h$ holes of size $m$ is sufficient in the case of block size three, except for a nonexisting $(6,3,1)$-PMD.