Lotto Designs

Abstract

Let $L(n,k,p,t)$ denote the minimum number of subsets of size $k$ ($k$-subsets) of a set of size $n$ ($n$-set) such that any $p$-subset intersects at least one of these $k$-subsets in at least $t$ elements. The value of $L(n,6,6,2)$ is determined for $n\le 54$.