A new example of non-amorphous association schemes

Abstract

E. R. van Dam gave an example of primitive non-amorphous
association schemes in which every nontrivial relation is a
strongly regular graph, as a fusion scheme of
the cyclotomic scheme of class $45$ on $¥GF(2^{12})$.
The aim of this paper is to present a new example of
primitive non-amorphous association schemes in which
every nontrivial relation is a strongly regular graph,
as a fusion scheme of the cyclotomic scheme of
class $75$ on $¥GF(2^{20})$. We also propose
an infinite family of parameters of association schemes
containing both of these two examples.