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 language | English |
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Pages (from-to) | 307-321 |
Number of pages | 15 |
Journal | Advances in Mathematics |
Volume | 335 |
Early online date | 17 Jul 2018 |
DOIs | |
Publication status | Published - 7 Sept 2018 |
Keywords
- Kissing numbers
- Spherical codes
- High dimensional geometry