On kissing numbers and spherical codes in high dimensions

Matthew Jenssen, Felix Joos, Will Perkins

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)
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Abstract

We prove a lower bound of Ω(d3/2·(2/√3)d) on the kissing number in dimension d. This improves the classical lower bound of Chabauty, Shannon, and Wyner by a linear factor in the dimension. We obtain a similar linear factor improvement to the best known lower bound on the maximal size of a spherical code of acute angle θ in high dimensions.
Original languageEnglish
Pages (from-to)307-321
Number of pages15
JournalAdvances in Mathematics
Volume335
Early online date17 Jul 2018
DOIs
Publication statusPublished - 7 Sep 2018

Keywords

  • Kissing numbers
  • Spherical codes
  • High dimensional geometry

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