Betke–Henk–Wills–Malikiosis discrete Minkowski conjecture

Let $K\in\mathcal K^n$ be a full-dimensional convex body and let $\Lambda\in\mathcal L^n$. Let $K_s$ be the symmetrization of $K$, and let $\operatorname{G}(K,\Lambda)=\#(K\cap\Lambda)$. Discrete Minkowski conjecture.

$$\operatorname{G}(K,\Lambda)\leq\prod_{i=1}^n\left\lfloor\frac{2}{\lambda_i(K_s,\Lambda)}+1\right\rfloor.$$

The source presents this as a conjectural strengthening of the known bound involving only the first successive minimum and gives no resolution.