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

We give a hierarchy of $k$-point bounds extending the Delsarte-Goethals-Seidel linear programming $2$-point bound and Bachoc-Vallentin semidefinite $3$-point for spherical codes. An optimized implementation this allows us to compute~$4$, $5$, $6$-point maximum number equiangular lines in Euclidean space with fixed common angle.