Nonexistence of Exceptional 5-class Association Schemes with Two $Q$-polynomial Structures

Understand

In [H.

• Suzuki, Association schemes with multiple $Q$-polynomial structures, J.
• Algebraic Combin.
• 7 (1998) 181-196], Suzuki gave a classification of association schemes with multiple $Q$-polynomial structures, allowing for one exceptional case which has five classes.