From the author’s introduction: “It is well known that the orbits of any automorphism group of a design D give rise to a tactical decomposition of D. In this paper we study the orbit decomposition given by a standard automorphism group of a point-divisible design and we prove that there is a rational congruence which is naturally associated to the decomposition. We note that it is possible to apply to this rational congruence the Hasse-Minkowski theory to obtain a non-existence theorem for standard automorphism groups of those designs. The theorem simultaneously generalizes the Bruck-Ryser-Chowla, Hughes, and Bose-Connor theorems.”