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arXiv · 1904.11462

Exponential improvements for superball packing upper bounds

Ashwin Sah·Mehtaab Sawhney·David Stoner·Yufei Zhao
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Abstract

We prove that for all fixed $p > 2$, the translative packing density of unit $\ell_p$-balls in $\mathbb{R}^n$ is at most $2^{(γ_p + o(1))n}$ with $γ_p < - 1/p$. This is the first exponential improvement in high dimensions since van der Corput and Schaake (1936).

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Ashwin Sah, Mehtaab Sawhney, David Stoner, Yufei Zhao. 2020-02-13. Exponential improvements for superball packing upper bounds. https://doi.org/10.1016/j.aim.2020.107056

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