Even when a parameter set (v, k, λ) satisfies the necessary conditions for the existence of a Balanced Incomplete Block (BIB) design, the actual design may not exist or its existence may be unknown.

Certain balanced incomplete block designs are such that a double grouping of blocks into sets made up of complete replications is possible, with a corresponding reduction in the variance of interblock ...

A graph G with vertex set V is said to be n-existentially closed (or n-e.c. for short) if, for every proper subset S of V with |S|=n and every subset T of S, there exists a vertex x in V-S such that x ...