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The kissing number of $\mathbb{R}^n$ is the maximum number ofpairwise-nonoverlapping unit spheres that can simultaneously touch a centralunit sphere. Mittelmann and Vallentin (2010), based on the semidefiniteprogramming bound of Bachoc and Vallentin (2008), computed the best known upperbounds for the kissing number for several values of $n \leq 23$. In this paper,we exploit the symmetry present in the semidefinite programming bound toprovide improved upper bounds for $n = 9, \ldots, 23$.

Improving the semidefinite programming bound for the kissing number by exploiting polynomial symmetry