Estimates for logarithmic and Riesz energies for spherical $t$-designs

In this paper we find asymptotic equalities for the discrete logarithmic energy of sequences of well separated spherical $t$-designs on the unit sphere ${\mathbb{S}^{d}\subset\mathbb{R}^{d+1}}$, $d\geq2$. Also we establish exact order estimates for discrete Riesz $s$-energy, $s\geq d$, of sequences of well separated spherical $t$-designs.