  An $(n,r,s)$-system is an $r$-uniform hypergraph on $n$ vertices such that
every pair of edges has an intersection of size less than $s$. Using
probabilistic arguments, R\"{o}dl and \v{S}i\v{n}ajov\'{a} showed that for all
fixed integers $r> s \ge 2$, there exists an $(n,r,s)$-system with independence
number $O\left(n^{1-\delta+o(1)}\right)$ for some optimal constant $\delta >0$
only related to $r$ and $s$. We show that for certain pairs $(r,s)$ with $s\le
r/2$ there exists an explicit construction of an $(n,r,s)$-system with
independence number $O\left(n^{1-\epsilon}\right)$, where $\epsilon > 0$ is an
absolute constant only related to $r$ and $s$. Previously this was known only
for $s>r/2$ by results of Chattopadhyay and Goodman
