Six-dimensional sphere packing and linear programming
arXiv:2211.09044 · doi:10.1090/mcom/3959
Abstract
We prove that the Cohn-Elkies linear programming bound for sphere packing is not sharp in dimension 6. The proof uses duality and optimization over a space of modular forms, generalizing a construction of Cohn-Triantafillou to the case of odd weight and non-trivial character.
arXiv comment36 pages, 3 figures, 3 tables, 3 supplementary text files; v3: corrected typos, simplified system (4.2) and equation (5.4); v4: same as v3 but more comments and two new formulas added to supplementary file
References in corpus (7)
- New upper bounds on sphere packings I
- The sphere packing problem in dimension 24
- The sphere packing problem in dimension 8
- Universally optimal distribution of points on spheres
- New upper bounds on sphere packings II
- Sphere packing bounds via spherical codes
- High-dimensional sphere packing and the modular bootstrap