The sphere packing problem in dimension 24
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In this article, it was shown that the Leech lattice is the densest packing of congruent spheres in twenty-four dimensions and that it is the unique optimal periodic packing.Abstract:
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.read more
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References
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Journal ArticleDOI
The sphere packing problem in dimension 8
TL;DR: In this article, it was shown that no packing of unit balls in Euclidean space with density greater than that of the lattice packing has density better than the E_8$-lattice packing.
Journal ArticleDOI
The sphere packing problem in dimension 8The sphere packing problem in dimension 8
TL;DR: In this paper, it was shown that no packing of unit balls in Euclidean space R-8 has density greater than that of the E8-lattice packing.
Journal ArticleDOI
Optimal asymptotic bounds for spherical designs
TL;DR: In this article, the conjecture of Korevaar and Meyers that for each N cdt d, there exists a spherical t-design in the sphere S d consisting of n points, where cd is a constant depending only on d.