The lattice is an exceptional lattice inside .
The -lattice may be presented as the linear span with integer coefficients of the following basis vectors in the real vector space :
If 7-spheres of radius are centered around every point of the lattice, then each sphere touches 240 other spheres.
A proof that this arrangement gives the optimal sphere packing in 8 dimensions was given in Viazovska (2016). (The analogous statement holds in 24 dimensions with respect to the Leech lattice [CKMRV17].)
The optimal sphere packing constant in 8 dimensions is
See also:
Discussion in relation to sphere packing:
Review:
Last revised on July 17, 2024 at 12:32:29. See the history of this page for a list of all contributions to it.