Zheng's realizability criterion for branch data

Let $d=d'd”$, where $d'$ is the minimal prime factor of $d$ and $d”>2$, so that $d$ is neither prime nor equal to $4$. Let $\mathcal{D}$ be branch data with $k$ partitions, and suppose it satisfies the Hurwitz condition. Zheng's realizability criterion. If $k>d”+1$, then $\mathcal{D}$ is realizable. Moreover, this bound is sharp: the displayed collection of partitions in the statement, with $k=d”+1$ and $\nu(\mathcal{D})=2d-2$, is non-realizable. This criterion gives a sufficient condition for realizability together with an explicit sharpness example; the source does not provide a separate resolution status for it.