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A new lower bound for sphere packing (2312.10026v1)
Published 15 Dec 2023 in math.MG, math.CO, and math.PR
Abstract: We show there exists a packing of identical spheres in $\mathbb{R}d$ with density at least [ (1-o(1))\frac{d \log d}{2{d+1}}\, , ] as $d\to\infty$. This improves upon previous bounds for general $d$ by a factor of order $\log d$ and is the first asymptotically growing improvement to Rogers' bound from 1947.
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