New Conjectural Lower Bounds on the Optimal Density of Sphere Packings

  title={New Conjectural Lower Bounds on the Optimal Density of Sphere Packings},
  author={Salvatore Torquato and Frank H. Stillinger},
  journal={Experimental Mathematics},
  pages={307 - 331}
Sphere packings in high dimensions interest mathematicians and physicists and have direct applications in communications theory. Remarkably, no one has been able to provide exponential improvement on a hundred-year-old lower bound on the maximal packing density due to Minkowski in d-dimensional Euclidean space ℝ d . The asymptotic behavior of this bound is controlled by 2-d in high dimensions. Using an optimization procedure that we introduced earlier [Torquato and Stillinger 02] and a… Expand
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