Association schemes from ovoids in $ PG(3,q) $

Abstract

We discuss three proofs of a conjecture of De Caen and Van Dam on the existence of some four-class association scheme on the set of unordered pairs of distinct points of the projective line \( \textit{PG}(1,4^f) \), where\( f\geq 2 \) is an integer. Our emphasis is on the proof using inversive planes and ovoids in \( PG(3,q) \).