Large automorphism groups compared to the $p$-rank of algebraic curves in characteristic $p$

Let $\cX$ be a (projective, geometrically irreducible, non-singular) algebraic curve of genus $\ge 2$ and positive $p$-rank $γ(\cX)$, defined over an algebraically closed field $\mathbb{K}$ of positive characteristic $p>0$. Contrary to what occurs for the genus, no function $h(γ)$ exists such that $