The dual Strong F-conjecture for the moduli space of pointed genus-zero curves

Let $\overline M_{0,n}$ be the moduli space of stable genus-zero curves with $n$ marked points. Let $\operatorname{PBDcone}(n)$ be the cone associated with effective partition block designs on $[n-1]$, identified with the dual of the effective boundary cone in $N_1(\overline M_{0,n})$. Dual Strong F-conjecture. For $n\leq 11$, $\operatorname{PBDcone}(n)$ is contained in the convex cone generated by the classes of F-curves in $N_1(\overline M_{0,n})$; equivalently, every extremal effective PBD on $[n-1]$ is an effective combination of F-curves. This is the dual formulation of the Strong F-conjecture in the stated range, and the supplied context does not indicate that it has been proved.