Nonexistence of exceptional imprimitive Q-polynomial association schemes with six classes

Understand

Suzuki (1998) showed that an imprimitive Q-polynomial association scheme with first multiplicity at least three is either Q-bipartite, Q-antipodal, or with four or six classes.

• The exceptional case with four classes has recently been ruled out by Cerzo and Suzuki (2009).
• In this paper, we show the nonexistence of the last case with six classes.
• Hence Suzuki's theorem now exactly mirrors its well-known counterpart for imprimitive distance-regular graphs.