We define a family of random sets of points, the Diamond ensemble, on the sphere S2 depending on several parameters. Its most important property is that, for some of these parameters, the asymptotic expected value of the logarithmic energy of the points can be computed rigorously and shown to attain very small values, quite close to the conjectured minimal value.
Etayo Rodriguez, M. D. U., & Beltran, C. (Accepted/In press). The Diamond ensemble: A constructive set of spherical points with small logarithmic energy. Journal of Complexity, . https://doi.org/10.1016/j.jco.2020.101471