2026
CLM-LR-DRAFT-E8-1= E8 packing optimumEXACT VALUEThe sphere packing problem in dimension 8Source: Optimal sphere packing in eight dimensions ↗
PROVEN
Limits RegistryPUBLIC RECORDLimits RegistryPUBLIC RECORDLimits RegistryPUBLIC RECORDLimits RegistryResearch Console →The sphere packing problem asks what fraction of space can be filled by non-overlapping equal spheres. In eight dimensions, the extraordinarily symmetric E8 lattice achieves the provably optimal arrangement — a landmark 2016 result.
The question, scope, and sources behind this Registry record.
What is the maximum density achievable by any packing of non-overlapping equal spheres in eight-dimensional Euclidean space?
In this paper we prove that no packing of unit balls in Euclidean space ℝ⁸ has density greater than that of the E₈-lattice packing.
Optimal sphere packing in eight dimensionsCurrent frontiers derived from accepted Claims.
The accepted equality closes this optimization result.
Assertions tied to evidence, attribution, and review.
The frontier as it changed over time.
Only accepted Claims matching the current specification contribute to the displayed bounds. Strict inequalities remain open; contradictory Claims require editorial review.