Exponential improvements for superball packing upper bounds

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 $2^{({\gamma }_p+o(1))n}$ with ${\gamma }_p<-1/p$. This is the first exponential improvement in high dimensions since van der Corput and Schaake (1936).

References in corpus (8)

• The sphere packing problem in dimension 24
• The sphere packing problem in dimension 8
• Optimal Packings of Superballs
• Novel Features Arising in the Maximally Random Jammed Packings of Superballs
• A conceptual breakthrough in sphere packing
• Sphere packing bounds via spherical codes
• The packing density of the $n$-dimensional cross-polytope
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Cited by in corpus (1)

• Bounds for Multiple Packing and List-Decoding Error Exponents