Benson's conjecture on the Loewy length of blocks

Let $G$ be a finite group and $B$ a block of $kG$ over a field $k$ of characteristic $p$, with defect group $D$. Benson's conjecture. The Loewy length of $B$ should satisfy

$$\operatorname{ll}(B)>p\text{-rank}(D).$$

This conjecture predicts a lower bound for the Loewy length of a block in terms of the $p$-rank of its defect group. Its resolution status is not established by the supplied text.