The existence of 23 ${2}^{3}$‐decomposable super‐simple (v,4,6) $(v,4,6)$‐BIBDs

Abstract

AbstractA design is said to be super‐simple if the intersection of any two blocks has at most two elements. A design with index is said to be ‐decomposable, if its blocks can be partitioned into nonempty collections , , such that each with the point set forms a design with index . In this paper, it is proved that there exists a ‐decomposable super‐simple ‐BIBD (balanced incomplete block design) if and only if and .