On the resolvent degree of PSU(3,q)

Resolvent degree ($\mathrm{RD}$) is an invariant of finite groups in terms of the complexity of their algebraic actions. We address the problem of bounding $\mathrm{RD}(G)$ for all finite simple groups using the methods established by Gómez-Gonzáles-Sutherland-Wolfson in terms of ${\mathrm{RD}}_{\mathbb{C}}^{\le d}$-versality and special points. We give upper bounds on $\mathrm{RD}(\mathrm{PSU}(3,q))$ and $\mathrm{RD}(\mathrm{PSU}(2,q))$ in terms of classical invariant theory. In the $\mathrm{PSU}(3,q)$ case, stability of low-degree invariants permit an asymptotic bound on $\mathrm{RD}$ growing in $q$.