SPHERE PACKING BOUNDS VIA SPHERICAL CODES

@article{Cohn2014SPHEREPB,
  title={SPHERE PACKING BOUNDS VIA SPHERICAL CODES},
  author={Henry Cohn and Y. Zhao},
  journal={Duke Mathematical Journal},
  year={2014},
  volume={163},
  pages={1965-2002}
}
The sphere packing problem asks for the greatest density of a packing of congruent balls in Euclidean space. The current best upper bound in all suciently high dimensions is due to Kabatiansky and Levenshtein in 1978. We revisit their argument and improve their bound by a constant factor using a simple geometric argument, and we extend the argument to packings in hyperbolic space, for which it gives an exponential improvement over the previously known bounds. Additionally, we show that the Cohn… Expand
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