Submitted:
02 May 2026
Posted:
05 May 2026
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Abstract
In the course of extending the obtained regularities of lattice packings corresponding to layered lattices of the “Lambda” series in dimensions 1–24 to groups of higher dimensions, a hypothesis was formulated about the density function of the densest lattice packing of equal spheres in n−dimensional Euclidean space. The hypothesis can be used as an approximate method for solving the problem of lattice packing of equal spheres in n−dimensional Euclidean space.
Keywords:
metric geometry
; geometric number theory
; lattice theory
; arithmetic minima of positive quadratic forms
; lattice packings of equal spheres
; Hermite constant
; computational mathematics
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