Three-class association schemes from partial geometric designs

Abstract

In this paper, we show that three-class association schemes can be constructed from certain partial geometric designs. First, we show that partial geometric designs with exactly three indices: r−n, λ1 and λ2 give rise to three-class association schemes, using the method of Beker and Haemers (1980). Second, we describe parameter sets of certain partial geometric designs that also give rise to three-class association schemes.