Existence of Indecomposable \(B[4 , 6; v]\) without Repeated Blocks

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