The existence of λ $\lambda $‐decomposable super‐simple (4,2λ) $(4,2\lambda )$‐GDDs of type gu ${g}^{u}$ with λ=2,4 $\lambda =2,4$

Abstract

AbstractA design is said to be super‐simple if the intersection of any two of its 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 for , there exists a ‐decomposable super‐simple ‐GDD of type if and only if , and , except for , and except possibly for .