Pseudocyclic 3-class association schemes on 28 points

Abstract

In [5], Mathon described a pseudocyclic symmetric 3-class association scheme on 28 points. In this paper we will first present a general method (a ‘switching’ construction) to construct new symmetric 3-class association schemes from old ones. This method is then applied to the scheme above and yields another scheme with the same parameters. A proof is sketched that these two schemes are the only pseudocyclic symmetric 3-class association schemes on 28 points. Also, a useful reformation is given of a known existence condition for general pseudocyclic symmetric 3-class association schemes.