This work is built upon a series of my previous works on distributing points on the unit sphere with various symmetry constraints. As mentioned in the paper, this type of uniform point set may be useful in a variety of scientific and engineering applications. My eventual goal is to apply this type of point set to better quantify the hemispheric asymmetry of the human brain. Interestingly, as kindly pointed out by one of the reviewers of my work (many thanks to the reviewers and to Prof. Bruce Boghosian of Tufts University, a member of the editorial board of Journal of Computational Science who handled my submission, for the excellent selection of reviewers), the vertical projections of the optimal configurations share apparent similarity with those of the minimum energy configurations of a system of 2D charged particles in a quadratic potential well.
Tabulated point sets from (N=2 to N=500) are available for download here. It is a zip file containing 499 text files. The first two lines in each file refer to the number of points and the minimum energy achieved, which is based on Eq.[1] in the paper.
If you are interested in generating some of the figures shown in the paper, you can download the original Mathematica notebook here and its PDF version here.