Six-dimensional sphere packing and linear programming
Matthew de Courcy-Ireland, Maria Dostert, Maryna Viazovska · Mathematics of Computation · 2024
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 [Math. Comp. 91 (2021), pp. 491–508] to the case of odd weight and non-trivial character.