  Let $h\geq 2$ be a positive integer. For any subset $\mathcal{A}\subset
\mathbb{Z}_n$, let $h^{\wedge}\mathcal{A}$ be the set of the elements of
$\mathbb{Z}_n$ which are sums of $h$ distinct elements of $\mathcal{A}$.
  In this paper, we obtain some new results on $4^{\wedge}\mathcal{A}$ and
$5^{\wedge}\mathcal{A}$. For example, we show that if $|\mathcal{A}|\geq
0.4045n$ and $n$ is odd, then $4^{\wedge}\mathcal{A}=\mathbb{Z}_{n}$; Under
some conditions, if $n$ is even and $|\mathcal{A}|$ is close to $n/4$, then
$4^{\wedge}\mathcal{A}=\mathbb{Z}_{n}$.
