In the past modular curves of various type (classical, Drinfeld, Shimura) have been used successfully to construct high genus curves with many rational points over finite fields of square cardinality. In this talk I will explain how Drinfeld modular varieties can be used similarly to obtain high genus curves over any non-prime finite field with many rational points. This way we obtain lower bounds for the Ihara constant A(q) for all non-prime q, which are better then all previously known bounds. This is joint work with Beelen, Garcia, Stichtenoth.