A Four-Class Subscheme of the Association Scheme Coming from the Action ofPGL(2, 4f)

Let Ω denote the set of two-element subsets of the projective line PG(1,q ), where q = 2e, e ≥ 1. The character table of the association scheme X(PGL(2, q), Ω) is calculated. Then by using this character table, we prove that the conjectured subscheme of de Caen and van Dam is indeed an association scheme.