I'm reading Raynaud's proof for the Abhyankar conjecture on $\mathbb{A}^1$, namely,
Let $k$ be an algebraically closed field of characteristic $p>0$. Then every quasi-$p$ group is the Galois group of some connected etale cover of $\mathbb A_k^1$.
But I could't find illustrative examples in the literature. There are some explicit examples in Abhyankar's old papers, but they look quite concise. In this 1992 paper, Abhyankar listed some Galois groups coming from certain types of equations, but the calculation are not fully showed (some of the them even involve the classifying result of finite simple groups).
So I wonder: is there some explicit examples in the literature, that can (partly) exhibit the spirit of Raynaud's proof? (Actually I would be glad to see a "computable" cover aside from the Artin-Schreier.) Any suggestion would be greatly appreciated.