  We show that there is no (75,32,10,16) strongly regular graph. The result is
obtained by a mix of algebraic and computational approaches. The main idea is
to build large enough induced structure and apply the star complement
technique. Our result implies that there is no regular two-graph on 76 vertices
and no partial geometry with parameters pg(4,7,2). In particular, it implies
that there is no (76,35,18,14) strongly-regular graph. In order to solve this
classification problem we also develop an efficient algorithm for the problem
of finding a maximal clique in a graph.
