Combinatorial designs with two singular values II. Partial geometric designs

Abstract

In this and an earlier paper [E.R. van Dam, E. Spence, Combinatorial designs with two singular values. I. Uniform multiplicative designs, J. Combin. Theory A 107 (2004) 127–142] we study combinatorial designs whose incidence matrix has two distinct singular values. These generalize ( v, k, λ) designs, and include uniform multiplicative designs and partial geometric designs. Here we study the latter, which are precisely the designs with constant replication and block size. We collect most known results, give new characterization results, and we enumerate, partly by computer, all small ones.