Estimates of the optimal density of sphere packings in high dimensions

in high dimensions A. Scardicchio, F. H. Stillinger, and S. Torquato Department of Physics, Joseph Henry Laboratories, Princeton University, Princeton, New Jersey 08544, USA Princeton Center for Theoretical Physics, Princeton University, Princeton, New Jersey 08544, USA Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544, USA Princeton Institute for the Science and Technology of Materials, Princeton University, Princeton, New Jersey 08544, USA School of Natural Sciences, Institute for Advanced Study, Princeton, New Jersey, 08540, USA