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On kissing numbers and spherical codes in high dimensions (1803.02702v2)
Published 7 Mar 2018 in math.MG, math.CO, and math.PR
Abstract: We prove a lower bound of $\Omega (d{3/2} \cdot (2/\sqrt{3})d)$ 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 $\theta$ in high dimensions.
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