Resolvable (r, λ)-designs and the Fisher inequality

It is well known that in any ( v, b, r, k, λ ) resolvable balanced incomplete block design that b≧ ν + r − l with equality if and only if the design is affine resolvable. In this paper, we show that a similar inequality holds for resolvable regular pairwise balanced designs ((ρ, λ)-designs) and we characterize those designs for which equality holds. From this characterization, we deduce certain results about block intersections in (ρ, λ)-designs.