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We prove a lower bound of $\Omega (d^{3/2} \cdot (2/\sqrt{3})^d)$ on thekissing number in dimension $d$. This improves the classical lower bound ofChabauty, Shannon, and Wyner by a linear factor in the dimension. We obtain asimilar linear factor improvement to the best known lower bound on the maximalsize of a spherical code of acute angle $\theta$ in high dimensions.

On kissing numbers and spherical codes in high dimensions