Weak Donovan conjecture on bounded Cartan invariants

Let $\ell$ be a prime, let $k$ be the coefficient field, and let $D$ be a finite $\ell$-group. For a finite group $G$, let $B$ be a block of $kG$ and let its Cartan matrix record the Cartan invariants of $B$.

Weak Donovan conjecture. There exists a constant $c(D)\in\mathbb N$ such that, if $G$ is a finite group and $B$ is a block of $kG$ with defect group isomorphic to $D$, then the entries of the Cartan matrix of $B$ are bounded by $c(D)$.

The source states that Donovan's conjecture is equivalent to this conjecture together with boundedness of Morita Frobenius numbers. The supplied context gives no resolution of the weak Donovan conjecture.