Upper bounds on the general covering number Cλ(v, k, t, m)

A collection C of k-subsets (called blocks) of a v-set X(v) = {1, 2,..., v} (with elements called points) is called a t-(v,k,m,lambda) covering if for every in-subset M of X(v) there is a subcollection K of C with \K\ greater than or equal to lambda such that every block K is an element of K has at least t points in common with M. It is required that v greater than or equal to k greater than or equal to t and v greater than or equal to m greater than or equal to t. The minimum number of blocks in a t- (v, k, m, lambda) covering is denoted by Clambda (v, k, t, m). We present some constructions producing the best known upper bounds on C-lambda (v, k, t, in) for k = 6, a parameter of interest to lottery players. (C) 2004 Wiley Periodicals, Inc.