On Some Tactical Configurations

Given a set E of v elements, and given positive integers k , l ( l ≤ k ≤ v ), and λ, we understand by a tactical configuration C [ k, l, λ, v ] (briefly, configuration ) a system of subsets of E , having k elements each, such that every subset of E having l elements is contained in exactly λ sets of the system. A necessary condition for the existence of a configuration C [ k, l, λ, v ] is known (6) to be