Let $A$ be a set of size $n$. Given a random seed $s$, I am looking to build a pseudo-random random permutation $\pi_s: A \rightarrow A$ such that $\pi_s(a)$ is fast to compute for every $a \in A$. By "fast to compute" I mean significantly faster than $O(n)$ time, e.g. $O(1)$ or $O(\log n)$ time.
One suggestion is to use Feistel networks or MiMC. Any other suggestions?