Spherical designs and its application

Abstract

In this thesis, we introduce the spherical designs and its applications. First application is to the study of the partial geometries. We show the nonexistence of Izo(r) for in nitely many r, which is an important families of partial geome- tries attaining Krein equality. Especially, our result contains the nonexistence of Izo(4), which was the rst open case. Second application is to the study of the set of the equiangular lines and the strongly regular graphs related to the set of the equiangular lines. I