In this and a sequel paper [10] we study combinatorial designs whose incidence matrix has two distinct singular values.These generalize 2-(v, k, É) designs, and include partial geometric designs and uniform multiplicative designs.Here we study the latter, which are precisely the nonsingular...

Suppose one looks for a square integral matrixN, for which NN has a prescribed form.Then the Hasse-Minkowski invariants and the determinant of NN lead to necessary conditions for existence.The Bruck-Ryser-Chowla theorem gives a famous example of such conditions in case N is the incidence matrix...

In this and an earlier paper [17] we study combinatorial designs whose incidence matrix has two distinct singular values.These generalize (v, k, ë) designs, and include uniform multiplicative designs and partial geometric designs.Here we study the latter, which are precisely the designs with...