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Packing spheres efficiently in large dimension $d$ is a particularlydifficult optimization problem. In this paper we add an isotropic interactionpotential to the pure hard-core repulsion, and show that one can tune it inorder to maximize a lower bound on packing density. Our results suggest thatexponentially many (in the number of particles) distinct disordered spherepackings can be effectively constructed by this method, up to a packingfraction close to $7\, d\, 2^{-d}$. The latter is determined by solving theinverse problem of maximizing the dynamical glass transition over the space ofthe interaction potentials. Our method crucially exploits a recent exactformulation of the thermodynamics and the dynamics of simple liquids ininfinite dimension.

Generating dense packings of hard spheres by soft interaction design