Fast Construction of Irreducible Polynomials of degree n over any Finite Field

[burritoloco]

Hello, I'm currently doing an undergrad project on this topic and I was wondering if any of you guys know what is the fastest algorithm (asymptotically) that has been discovered so far, for such purpose. Here is paper by Shoup (1993) which gave the fastest algorithm up to then.

http://www.shoup.net/papers/fastirred.pdf

After that, I'm not really sure. Any ideas? Thank you.

 

[burritoloco]

Just found this paper by Jean-Marc Couveignes and Reynald Lercier (2009):

http://www.math.univ-toulouse.fr/~couveig/publi/couveignes-lercier.pdf