The sphere packing problem in dimension 24
By Henry Cohn, Abhinav Kumar, Stephen D. Miller, Danylo V. Radchenko, Maryna S. Viazovska. 2016
211 citations recorded by the source corpus.
Building on Viazovska's recent solution of the sphere packing problem in eight dimensions, we prove that the Leech lattice is the densest packing of congruent spheres in twenty-four dimensions and that it is the unique optimal periodic packing. In particular, we find an optimal auxiliary function for the linear programming bounds, which is an analogue of Viazovska's function for the eight-dimensional case.
Subfields: Applied Mathematics, Computer Vision and Pattern Recognition, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/1dee625271b3cf88b7e41b22399c3b1c92ab68cd
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Citations in the corpus
- Minimax and maximin space-filling designs: some properties and methods for construction (2017, unknown): “The construction presented here is based on the developments in (Gauthier and Pronzato, 2014, 2016), following the original ideas of Fedorov (1996), and is motivated by the connection between minimax-optimal design and minimisation of the maximum kriging variance, see Section 2.5.2.”
- QuIP#: Even Better LLM Quantization with Hadamard Incoherence and Lattice Codebooks (2024, methodology): “To quantize incoherent matrices, QuIP # uses the BlockLDLQ block adaptive rounding algorithm with compressible codebooks based on the E 8 lattice, which achieves the highest density 8 dimensional unit-ball packing (Viazovska, 2017) (Section 4).”
- Hyperuniform states of matter (2018, background): “(Note it was recently proved that the E8 and L24 lattices are the densest packings among all possible packings in dimensions 8 [153] and 24 [154], respectively.”