In this paper we construct Galois towers with good asymptotic properties over
any non-prime finite field Fℓ; i.e., we construct sequences of
function fields N=(N1⊂N2⊂⋯) over Fℓ of increasing genus, such that all the extensions Ni/N1 are
Galois extensions and the number of rational places of these function fields
grows linearly with the genus. The limits of the towers satisfy the same lower
bounds as the best currently known lower bounds for the Ihara constant for
non-prime finite fields. Towers with these properties are important for
applications in various fields including coding theory and cryptography