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Limits RegistryWeeks after Viazovska's 8-dimensional result, she and coauthors Henry Cohn, Abhinav Kumar, Stephen D. Miller, and Danylo Radchenko extended the same modular-forms technique to prove the Leech lattice is the optimal sphere packing in 24 dimensions, published in 2017. Dimensions 8 and 24 remain the only dimensions above 3 where the optimal sphere packing has been rigorously proven.
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Weeks after Viazovska's 8-dimensional result, she and coauthors Henry Cohn, Abhinav Kumar, Stephen D. Miller, and Danylo Radchenko extended the same modular-forms technique to prove the Leech lattice is the optimal sphere packing in 24 dimensions, published in 2017. Dimensions 8 and 24 remain the only dimensions above 3 where the optimal sphere packing has been rigorously proven.
The Leech lattice sphere packing achieves the maximum possible density of any arrangement of non-overlapping equal spheres in 24-dimensional Euclidean space.
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Limits Registry. LR-SPHERE-PACKING-DIMENSION-24. Optimal sphere packing in 24 dimensions (Leech lattice). 2026.