Existence of IPBDs of Block Size Four

Abstract

In this paper we prove that a $(v,u;\{4\},3)$-IPBD exists when $v,u\equiv 2$ or $3(\mathrm{mod}4)$ and $v\ge 3u+1$, and then solve the problem of the existence of $(v,u;\{4\},\lambda )$-IPBD completely, which generalizes the result of $[7]$.