On rational embeddings of curves in the second Garcia–Stichtenoth tower

In 1995, Garcia and Stichtenoth explicitly constructed a tower of projective curves over a finite field with q2 elements which reaches the Drinfeld–Vlăduţ bound. These curves are given recursively by covers of Artin–Schreier type where the curve on the nth level of the tower has a natural model in . In this paper, for q an even prime power, we use point projections in order to embed these curves into projective space of the lowest possible dimension.