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arXiv · 1803.02702

On kissing numbers and spherical codes in high dimensions

Matthew Jenssen·Felix Joos·Will Perkins
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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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Matthew Jenssen, Felix Joos, Will Perkins. 2018-03-07. On kissing numbers and spherical codes in high dimensions. https://arxiv.org/abs/1803.02702

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