On some covering designs (Q1065807)

An (n,k,t)-covering of a set X of cardinality n is a family \(F=\{B_ 1,B_ 2,...,B_ m\}\) of subsets of X each of cardinality k such that every t-tuple of X occurs in at least one subset \(B_ i\). Let C(n,k,t) denote the smallest integer m such that an (n,k,t) covering exists. A characterization of n, k values such that \(C(n,k,t)=m\), where \(3(t+1)/2<m\leq 3(t+2)/2\) is discussed in this paper.