geometry-topology / Sphere packing
Can a Cohn-Elkies auxiliary function certify the best known sphere packing in dimension $36$ as optimal? No. An explicit dual-feasible point for the Cohn-Elkies linear program, built from weight-$18$ modular forms for $\Gamma_0(24)$, shows the two-point linear programming bound in dimension $36$ exceeds the density of the Kschischang-Pasupathy packing by a factor of at least $32.91$.
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rules out the two-point LP method in this dimension; the optimal packing in dimension 36 remains unknown
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Can a Cohn-Elkies auxiliary function certify the best known sphere packing in dimension $36$ as optimal? No. An explicit dual-feasible point for the Cohn-Elkies linear program, built from weight-$18$ modular forms for $\Gamma_0(24)$, shows the two-point linear programming bound in dimension $36$ exceeds the density of the Kschischang-Pasupathy packing by a factor of at least $32.91$.
rules out the two-point LP method in this dimension; the optimal packing in dimension 36 remains unknown
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