A simplified proof for the limit of a tower over a cubic finite field

Recently Bezerra, Garcia and Stichtenoth constructed an explicit tower F=(Fn)n⩾0 of function fields over a finite field Fq3, whose limit λ(F)=limn→∞N(Fn)/g(Fn) attains the Zink bound λ(F)⩾2(q2−1)/(q+2). Their proof is rather long and very technical. In this paper we replace the complex calculations in their work by structural arguments, thus giving a much simpler and shorter proof for the limit of the Bezerra, Garcia and Stichtenoth tower.