Betke–Henk–Wills discretized second Minkowski conjecture

Let $K\subset\mathbb{R}^d$ be a centrally symmetric convex body, let ${\mathcal L}\subset\mathbb{R}^d$ be a lattice, and let $\lambda_k(K,\mathcal L)$ be its successive minima. Betke–Henk–Wills conjecture.

$$\left|K\cap{\mathcal L}\right|\leq\prod_{k=1}^d\left\lfloor\frac{2}{\lambda_k(K,\mathcal L)}+1\right\rfloor.$$

This is proposed as a discrete analogue of Minkowski's second theorem, and the source says it remains open in dimensions $d\geq4$.