Brauer height-set conjectures for nonabelian defect groups

Let $G$ be a finite group, let $p$ be a prime, and let $B$ be a $p$-block of $G$ with defect group $D$. Write $\operatorname{ht}(B)$ for the set of heights of the irreducible characters in $B$, and define $b$ and $e$ by

$$p^b=\max\operatorname{cd}(D),\qquad e=\max\operatorname{ht}(B).$$

Brauer height-set conjectures. The derived length $\operatorname{dl}(D)$ is bounded in terms of $e$; $b$ is bounded in terms of $e$; and $\operatorname{dl}(D)$ is bounded in terms of $|\operatorname{ht}(B)|$. Moreover, the bounds in the first and third assertions should be logarithmic. The source reports proofs for general linear groups and symmetric groups, but says that the conjectures have not been widely explored in general.