Nearly Sharp Bounds for Lattice Coverings by Convex Bodies

Heng Li, Xizhi Liu

For an $n$-dimensional convex body $K$, let ${\theta }_L(K)$ denote its lattice covering density, and let ${\Theta }_L^{\mathrm{conv}}(n)$ and ${\Theta }_L^{\mathrm{sym}}(n)$ be the corresponding worst-ca…