Corpus ID: 202558910

Dual linear programming bounds for sphere packing via modular forms.

@inproceedings{Cohn2019DualLP,
  title={Dual linear programming bounds for sphere packing via modular forms.},
  author={Henry Cohn and Nicholas Triantafillou},
  year={2019}
}
  • Henry Cohn, Nicholas Triantafillou
  • Published 2019
  • Mathematics
  • We obtain new restrictions on the linear programming bound for sphere packing, by optimizing over spaces of modular forms to produce feasible points in the dual linear program. In contrast to the situation in dimensions 8 and 24, where the linear programming bound is sharp, we show that it comes nowhere near the best packing densities known in dimensions 12, 16, 20, 28, and 32. More generally, we provide a systematic technique for proving separations of this sort. 

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