… Using Proposition 2.1, we can in principle now describe the tower of function fields of the
modular curves (𝑋0(𝑇𝑛))𝑛≥0. However, we can use Proposition 2.3 to find a recursive …

… explicit example of an asymptotically good tower for all non-prime fields q . In this … function
field F/q having at least one rational place can be embedded into an asymptotically good tower…

… good towers are rare. While the first examples were non-explicit, we focus on explicit towers
of function fields, that is towers where … It is known that if the field of constants of the tower has …

… Function field case We will fix a finite field IFqand ask how large the group of rational points
X (IFq) of a smooth absolutely irreducible algebraic curve X of genus 9 over IFq can be as 9 …

… the function field Fi at step i of a tower if we know the possible residue classes of places of
the function field Fi+1 … good, it must be defined over a finite field of cardinality exceeding 225. …

… of towers of function fields over Fl ; ie, we consider sequences F1 F2 F3 }}} of function fields
… We do not know any explicit example of an asymptotically good tower of function fields over …

… tower of function fields F0 ⊂ F1 ⊂ ... over a finite field such that every place of every Fi ramifies
in the tower … An asymptotically good tower of curves over the field with eight elements. Bull…

… For applications to coding theory though, explicit towers are needed. In [6], a tower of function
fields over Fq is defined to … Stichtenoth, Asymptotically good towers of function fields over …

… a field of characteristic zero and k(t) the rational function field … ranks of elliptic curves in towers
of function fields such as k(t1/… the tower of function fields K = k(t1/pr ) with r ≥ 1 or the tower …

… explicit “asymptotically good” Garcia-Stichtenoth (GS for short) tower of function … towers of
function fields: the Hermitian tower [12] and the asymptotically optimal GarciaStichtenoth tower […