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 (2¹2). 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 (2²0). We also propose an infinite family of parameters of association schemes containing both of these two examples.
Munemasa et al. (Mon,) studied this question.