Density–kissing-number relation for Euclidean balls

Establish or refute the conjectured asymptotic relation δ(Bⁿ) ≪ κ(Bⁿ)/2ⁿ between the translative packing density and translative kissing number of the n-dimensional unit ball.

Background

The paper compares known asymptotic upper bounds for the kissing number κ(Bⁿ) and packing density δ(Bⁿ). These estimates suggest that the density may be bounded, up to the paper’s asymptotic notation, by the kissing number divided by 2ⁿ.

The authors explicitly state that this relationship is unproven. It is therefore an unresolved conjectural connection between two central extremal quantities in sphere packing.