# Exponential improvements for superball packing upper bounds

## TL;DR

This paper establishes the first exponential improvement in upper bounds for the packing density of unit b5c1-balls in high-dimensional spaces for all fixed p > 2, advancing understanding of geometric packing limits.

## Contribution

It proves a new exponential upper bound on translative packing density of b5c1-balls in b5c4-dimensional space for all p > 2, improving previous bounds since 1936.

## Key findings

- New exponential upper bounds for packing densities
- First such improvements since 1936
- Bound b3_p < -1/p for all p > 2

## 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).