Parallel 2-partitioned configuration conjecture

Let $(\mathcal P,\mathcal H)$ be a point-hyperplane configuration in $\mathbb R^d$, with $\mathcal B(\mathcal H)$ its set of hyperplane offsets. A parallel 2-partitioned configuration is one in which the hyperplanes can be partitioned into pairs of parallel hyperplanes covering the points, and assume $\mathcal B(\mathcal H)=\{0,1\}$.

Parallel 2-partition conjecture. Then

$$\operatorname{rs}(\mathcal P,\mathcal H) \geq mn\cdot 2^{-\operatorname{polylog}(d)}.$$

The source states that this conjecture is equivalent to the log-rank conjecture. Thus it remains open unless the log-rank conjecture is resolved.