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

A collection $\cal C$ 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 , λ) covering if for every m ‐subset M of X ( v ) there is a subcollection $\cal K$ of $\cal C$ with $|\cal K|\geq \lambda$ such that every block K  ∈  $\cal K$ has at least t points in common with M . It is required that v  ≥  k  ≥  t and v  ≥  m  ≥  t . The minimum number of blocks in a t ‐( v , k , m , λ) covering is denoted by C λ ( v , k , t , m ). We present some constructions producing the best known upper bounds on C λ ( v , k , t , m ) for k  = 6, a parameter of interest to lottery players. © 2004 Wiley Periodicals, Inc.