Dual linear programming bounds for sphere packing via modular forms

Cohn, Henry; Triantafillou, Nicholas

doi:10.1090/mcom/3662

Dual linear programming bounds for sphere packing via modular forms
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by Henry Cohn and Nicholas Triantafillou HTML | PDF

Math. Comp. 91 (2022), 491-508 Request permission

Abstract:

We obtain new restrictions on the linear programming bound for sphere packing, by optimizing over spaces of modular forms to produce feasible points in the dual linear program. In contrast to the situation in dimensions $8$ and $24$, where the linear programming bound is sharp, we show that it comes nowhere near the best packing densities known in dimensions $12$, $16$, $20$, $28$, and $32$. More generally, we provide a systematic technique for proving separations of this sort.

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