Links between orthogonal arrays, association schemes and partial geometric designs

In this paper, we show how certain three-class association schemes and orthogonal arrays give rise to partial geometric designs. We also investigate the connections between partial geometric designs and certain regular graphs having three or four distinct eigenvalues, three-class association schemes, orthogonal arrays of strength two and particular linear codes. We give various characterizations of these graphs, association schemes and orthogonal arrays in terms of partial geometric designs. We also give a list of infinite families of directed strongly regular graphs arising from the partial geometric designs obtained in this paper.
Comment: 22 pages. This article is based on the talk presented by the third author at the International conference on Modern Trends in Algebraic Graph Theory, held in June 2 - 5, 2014 at Villanova University