On Resolvable BIBDs with Block Size Five

Abstract

It is shown that a resolvable BIBD with block size five and index two exists whenever $v\equiv 5(\mathrm{mod}10)$ and $v\ge 50722395$. This result is based on an updated result on the existence of a BIBD with block size six and index unity, which leaves $88$ unsolved cases. A construction using difference families to obtain resolvable BIBDs is also presented.