Discrepancy, separation and Riesz energy of finite point sets on the unit sphere

For d ≥ 2 we consider asymptotically equidistributed sequences of S_d codes, with an upper bound δ on spherical cap discrepancy, and a lower bound Δ on separation. For such sequences, if 0 < s < d, then the difference between the normalized Riesz s energy of each code, and the normalized s-energy double integral on the sphere is bounded above by O(δ^1-s/dΔ^-sN^-s/d where N is the number of code points. For well separated sequences of spherical codes, this bound becomes δ^1-s/d We apply these bounds to minimum energy sequences, sequences of well separated spherical designs, sequences of extremal fundamental systems, and sequences of equal area points.