Let $p$ be prime number and let $A$ be a $k$-elements subset of $\mathbb{Z}/p\mathbb{Z}$. Dias da Silva - Hamidoune Theorem states that $|h^{\hat{}}A| \geq \min(p, hk -h^2 + 1)$, where $h$ is an integer with $2 \leq h \leq k$ and $h^{\hat{}}A$ denote the set of all sums of $h$ distinct elements of $A$. What is/are the characterization of the set $A$ for which $|h^{\hat{}}A|$ attains the lower bound ? In other words, is the lower bound optimal in the above theorem ?

I know that the equality occurs for arithmetic progressions in case of $h = 2$.