Existence of Indecomposable $B[4,6;v]$ without Repeated Blocks

Abstract

It is proved in this paper that there exists a simple $B[4,6;v]$ for every $v\ge 6$. It is also proved that there exists an indecomposable simple $B[4,6;v]$ for every $v\ge 6,v\notin \{12,13,16,17,20\}$.