New upper bound for lattice covering by spheres

Jun Gao, Xizhi Liu, Oleg Pikhurko +1

We show that there exists a lattice covering of ${\mathbb{R}}^n$ by Eucledian spheres of equal radius with density $O\left(n{\ln }^{\beta }n\right)$ as $n\to \infty$, where \begin{align*} β:= \…