On the small covering numbers $g^{(5)}_1(v)$

Forbes, Anthony; Grannell, Mike; Griggs, Terry and Stanton, R. G. (2007). On the small covering numbers $g^{(5)}_1(v)$ . Utilitas Mathematica, 74, pp. 77–96.

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 $g^{(5)}_1(v)$ . As a prelude to further work, we give the values of $g^{(5)}_1(v)$ for $v\le 25$ , and construct all designs which attain this bound.