Upper bounds given by equitable partitions of a primitive association scheme

Suppose that (X,G)(X,G) is a primitive association scheme with |G|≥3|G|≥3 and ππ is an equitable partition of (X,G)(X,G) with |π|<|X||π|<|X|. We put π∗≔{C∈π∣|C|>1}π∗≔{C∈π∣|C|>1} and supp(π)≔⋃C∈π∗C. In this article we prove that |G|≤|supp(π)|−|π∗|+1, and show a necessary and sufficient condition for the equality to hold.