A counterexample to Ryser's covering conjecture

For every sufficiently large prime $s\equiv 2(\mathrm{mod}3)$ and every sufficiently large odd integer n, with the threshold depending on s, we construct an intersecting $(s^n+1)$-partite $(s^n+1)$-uniform hypergraph with covering number $s^n+1$. This disproves Ryser's covering conjecture in its intersecting case.