Pseudocyclic association schemes arising from the actions of PGL(2,m2) and PΓL(2,m2)

The action of PGL(2,m2) on the set of exterior lines to a nonsingular conic in PG(2,m2) affords an association scheme, which was shown to be pseudocyclic in [H.D.L. Hollmann, Association schemes, Master thesis, Eindhoven University of Technology, 1982]. It was further conjectured in [H.D.L. Hollmann, Association schemes, Master thesis, Eindhoven University of Technology, 1982] that the orbital scheme of PΓL(2,m2) on the set of exterior lines to a nonsingular conic in PG(2,m2) is also pseudocyclic if m is an odd prime. We confirm this conjecture in this paper. As a by-product, we obtain a class of Latin square type strongly regular graphs on nonprime-power number of points.