A set of points with optimal $L^2$ spherical cap discrepancy

We introduce an explicit deterministic collection of $N$ spherical points, $\cP_N\subset\mathbb S^2$, that we call the {\em deterministic Diamond points}. For every $00$ such that \[ 0\leq \frac{2^{α+1}}{α+2}N^2-\sum_{x,y\in\cP_N}|x-y|^α\le C_αN^{1-α/