One of the reasons why this field is still so active is because different measures and methods often result in slightly different optimal configurations. In the case of this post, I focused on direct construction methods; and measures relating to minimum distance or convex hulls.

For an excellent commentary on the latest for optimal Riesz energy (which includes Coulomb potentials) configurations can be found in the first paper that I reference: "A comparison of popular point configurations on S2", by Hardin, Michaels and Saff.