Betke–Henk–Wills–Malikiosis discrete analogue of Minkowski's second theorem

Let $K\subseteq\mathbb{R}^d$ be a convex body, let $\Lambda<\mathbb{R}^d$ be a lattice, and let $\lambda_1\le\cdots\le\lambda_d$ be the successive minima of $K$ with respect to $\Lambda$, defined by

$$\lambda_i=\inf\left\{\lambda>0:\dim\operatorname{span}_{\mathbb{R}}\left(\frac{\lambda}{2}(K-K)\cap\Lambda\right)\ge i\right\}.$$

Betke–Henk–Wills–Malikiosis conjecture. One has

$$\#(K\cap\Lambda)\le\prod_{i=1}^d\left\lfloor\frac{2}{\lambda_i}+1\right\rfloor.$$

This is the discrete analogue of Minkowski's second theorem, replacing the volume of a convex body by the number of lattice points it contains. Betke, Henk and Wills originally conjectured the inequality for origin-symmetric convex bodies, while Malikiosis conjectured that it remains valid without the symmetry assumption; the stated general version is open.