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We define a family of random sets of points, the Diamond ensemble, on thesphere $\mathbb{S}^{2}$ depending on several parameters. Its most importantproperty is that, for some of these parameters, the asymptotic expected valueof the logarithmic energy of the points can be computed rigorously and shown toattain very small values, quite close to the conjectured minimal value.

The Diamond ensemble: a constructive set of points with small logarithmic energy