There is no strongly regular graph with parameters (460, 153, 32, 60)

Andriy Bondarenko, Anton Mellit, Andriy Primak, Danylo Radchenko, Maryna Viazovska

Abstract

We prove that there is no strongly regular graph (SRG) with parameters (460, 153, 32, 60). The proof is based on a recent lower bound on the number of 4-cliques in a SRG and some applications of Euclidean representation of SRGs.