Puig's weak conjecture on source algebra dimensions

Let $G$ be a finite group, $D$ a defect group, $B$ a block algebra, and ${\cal B}$ the corresponding block. Write

$${\mathbb{F}}\Lambda={\mathbb{F}}\otimes_{\cal O}\Lambda$$

for a finitely generated algebra $\Lambda$ over ${\cal O}$. The algebra ${\mathbb{F}}B$ is the source $D$-algebra of the block algebra ${\mathbb{F}}{\cal B}$. Weak Puig Conjecture. Fixing $D$, there is a bound on the dimension of ${\mathbb{F}}B$. This is presented as a conjecture equivalent to Puig's Conjecture under an assertion stated in Th'evenaz. Its status is not specified in the source.