Some Infinite Families of Large Sets of t-Designs

摘要

A set of necessary conditions for the existence of a large set of t-designs, LS[N] (t, k, v), is N|(_(k - i)~(v - i)) for i = 0, 1, ..., t. We show that these conditions are sufficient for N = 3, t = 2, 3, or 4, and k <= 8.