Analysis of Conjectural Improvements to Minkowski's Lower Bound on the Sphere Packing Density

Torquato and Stillinger used a pair-correlation-function optimization framework to conjecture an exponential improvement of Minkowski's lower bound on the maximal density of sphere packings in $\mathbb{R}^d$, with rate $2^{-(0.7786524795\ldots+o(1))d}$. Conditional on their realizability conjecture,