Conjecture on character degrees and block heights

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 $B$. Character-degree/block-height conjecture. Then

$$|\operatorname{cd}(D)|\le|\operatorname{ht}(B)|+1.$$

The source calls this the block version of the Isaacs–Navarro–Tiep conjecture and gives only special-case evidence, so it remains open.