Three-point bounds for sphere packing

About

We define three-point bounds for sphere packing that refine the linear programming bound, and we compute these bounds numerically using semidefinite programming by choosing a truncation radius for the three-point function. As a result, we obtain new upper bounds on the sphere packing density in dimension 4 through 7 and 9 through 16. We also give a different three-point bound for lattice packing and conjecture that this second bound is sharp in dimension 4.

Henry Cohn, David de Laat, Andrew Salmon · 2022

Related benchmarks

Task	Dataset	Result
Sphere-packing density upper bound estimation	Sphere packing Dimension 4	Sphere Packing Density Upper Bound (D=4)63.610733	3
Sphere-packing density upper bound estimation	Sphere packing Dimension 5	Density Upper Bound0.51264513	3
Sphere-packing density upper bound estimation	Sphere packing Dimension 6	Upper Bound Density0.41030328	3
Sphere-packing density upper bound estimation	Sphere packing Dimension 7	Sphere Packing Density Upper Bound0.32114711	3
Sphere-packing density upper bound estimation	Sphere packing Dimension 9	Upper Bound Density (D=9)0.19112042	3
Sphere-packing density upper bound estimation	Sphere packing Dimension 10	Density Upper Bound0.14341009	3
Sphere-packing density upper bound estimation	Sphere packing Dimension 11	Upper Bound Density0.10672529	3
Sphere-packing density upper bound estimation	Sphere packing Dimension 12	Density Upper Bound0.07971177	3
Sphere-packing density upper bound estimation	Sphere packing Dimension 13	Density Upper Bound0.06016444	3
Sphere-packing density upper bound estimation	Sphere packing Dimension 14	Density Upper Bound0.04506122	3