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On kissing numbers and spherical codes in high dimensions
Matthew Jenssen, Felix Joos, Will Perkins · 2018-03-07 · via math.PR updates on arXiv.org

We prove a lower bound of $Ω(d^{3/2} \cdot (2/\sqrt{3})^d)$ 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 $θ$ in high dimensions.

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