The covering-radius conjecture for lattice zonotopes in general linear position

Let $S=\{\boldsymbol{z}_1,\dotsc,\boldsymbol{z}_m\}\subseteq\mathbb{Z}^n$ and let $Z$ be the lattice zonotope generated by $S$. The set $S$ is in LGP (general linear position) when every subset of at most $n$ vectors is linearly independent. The covering-radius conjecture. If $S$ is in LGP, then

$$\mu(Z)\leq\frac{n}{m}.$$

This would sharpen the asymptotic bounds for covering radii of lattice zonotopes and, through the paper's equivalences, improve the corresponding bounds for billiard-ball motions and view-obstruction problems. The source gives no resolution evidence.