Theorem: Assuming that the generalized Riemann hypothesis is true, there is a deterministic polynomial time algorithm to find an irreducible polynomial of degree $n$ over $\mathbb{F_p}$ The algorithm uses $O(n^6(\log p+\log n)^4(\log p)^2)$ bit operations.
My question : What is the most efficient algorithm for constructing an irreducible polynomial ?
I have found this document very informative, but it is about probabilistic algorithms.