Spherical t-designs which are orbits of finite groups

Abstract

A spherical t-design in $R^{d}$ is a finite nonempty subset $X$ in the unit sphere $\Omega_{d}=\{(x_{1}, --, x_{d})\in R^{d}|x_{1}^{2}+\cdots+x_{d}^{2}=1\}$ such that (0.1)