New upper bounds on sphere packings I

About

We develop an analogue for sphere packing of the linear programming bounds for error-correcting codes, and use it to prove upper bounds for the density of sphere packings, which are the best bounds known at least for dimensions 4 through 36. We conjecture that our approach can be used to solve the sphere packing problem in dimensions 8 and 24.

Henry Cohn, Noam Elkies · 2001

Related benchmarks

Task	Dataset	Result
Sphere-packing density upper bound estimation	Sphere packing Dimension 4	Sphere Packing Density Upper Bound (D=4)64.771	3
Sphere-packing density upper bound estimation	Sphere packing Dimension 5	Density Upper Bound0.52498	3
Sphere-packing density upper bound estimation	Sphere packing Dimension 6	Upper Bound Density0.41767	3
Sphere-packing density upper bound estimation	Sphere packing Dimension 7	Sphere Packing Density Upper Bound0.32746	3
Sphere-packing density upper bound estimation	Sphere packing Dimension 9	Upper Bound Density (D=9)0.19456	3
Sphere-packing density upper bound estimation	Sphere packing Dimension 10	Density Upper Bound0.14759	3
Sphere-packing density upper bound estimation	Sphere packing Dimension 11	Upper Bound Density0.11169	3
Sphere-packing density upper bound estimation	Sphere packing Dimension 12	Density Upper Bound0.08378	3
Sphere-packing density upper bound estimation	Sphere packing Dimension 13	Density Upper Bound0.06248	3
Sphere-packing density upper bound estimation	Sphere packing Dimension 14	Density Upper Bound0.04637	3