Covering product conjecture

Let $K$ be a convex body in $\mathbb{R}^n$ and let $\Lambda$ be a lattice in $\mathbb{R}^n$. Let $\mu_i(K,\Lambda)$ denote the covering minima.

Covering product conjecture. One has

$$\frac{n+1}{2^n}\prod_{i=1}^n\frac{1}{\mu_i(K,\Lambda)}\leq\frac{\operatorname{vol}(K)}{\det(\Lambda)},$$

and this bound is best possible.

The conjecture is presented as a covering-minima analogue of the volume inequalities for packing minima and is attributed to the cited work. Its validity is not resolved in the source.