Brauer's weak Donovan conjecture on Cartan invariants

Let $D$ be a finite $\ell$-group. For a block of a finite group with defect group $D$, let its Cartan invariants be the entries of its Cartan matrix.

Brauer's weak Donovan conjecture. There is a bound on the Cartan invariants of blocks of finite groups with defect group $D$ that depends only on $D$.

This is the weak form of Donovan's conjecture considered in the paper. The source's abstract and introduction state that the bound is established for arbitrary abelian $2$-groups, while the formulation itself allows general finite $\ell$-groups.