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

The minimum number of blocks having maximum size pre- cisely 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 25, and construct all designs which attain this bound.