On the small covering numbers g1(5) (v)

Abstract

The minimum number of blocks having maximum size precisely five that is required to cover, exactly once, all pairs of elements from a set of cardinality v is denoted by g₁⁽⁵⁾ (v). As a prelude to further work, we give the values of g₁⁽⁵⁾ (v) for v ≤ 25, and construct all designs which attain this bound.