The average kissing number 
is the supremum of the
average degrees of the contact graphs of nonempty
finite packings of balls in 
with pairwise disjoint interiors. The balls may have different
radii. Two balls are adjacent in the contact graph
when they touch, so a packing of 
balls with 
contacts has average degree 
(Dostert et al. 2022). This differs from the kissing number, which concerns congruent balls around
a single congruent ball.
Bockhaus and Glazyrin (2026) proved 
and 
. Finite portions of the 
and Leech lattice packings
approach these values. Bockhaus and Glazyrin (2026) also obtained the upper bounds
and 
using semidefinite programming. They
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