Almost Resolvable BIBDs with Block-Size $5$ or $6$

Abstract

An obvious necessary condition for the existence of an almost resolvable $B(k,k-1;v)$ is $v\equiv 1(\mathrm{mod}k)$. We show in this paper that the necessary condition is also sufficient for $k=5$ or $k=6$, possibly excepting $8$ values of $v$ when $k=5$ and $3$ values of $v$ when $k=6$.