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

When does a sequence of spherical codes with “good” spherical cap discrepancy, and “good” separation also have “good” Riesz s-energy? For d > 2 and the Riesz s-energy for 0 < s < d, we consider asymptotically equidistributed sequences of S codes with an upper bound δ on discrepancy and a lower bound ∆ on separation. For such sequences, the difference between the normalized Riesz s-energy and the normalized energy double integral is bounded above by O ` δ1−s/d ∆−s N−s/d ́ , where N is the number of code points. For well separated sequences of spherical codes, this bound becomes O ` δ1−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.