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Semidefinite programming bounds for the average kissing number

The average kissing number of $\mathbb{R}^n$ is the supremum of the average degrees of contact graphs of packings of finitely many balls (of any radii) in $\mathbb{R}^n$. We provide an upper bound for the average kissing number based on semidefinite programming that improves previous bounds in dimensions $3, \ldots, 9$. A very simple upper bound for the average kissing number is twice the kissing number; in dimensions $6, \ldots, 9$ our new bound is the first to improve on this simple upper bound.