On the spectrum for the genera of maximal curves over small fields

Abstract

Motivated by previous computations in Garcia, Stichtenoth and Xing (2000) paper ,we discuss the spectrum $\mathbf{M}(q^2)$ for the genera of maximal curves over finite fields of order $q^2$ with $7\leq q\leq 16$. In particular, by using a result in Kudo and Harashita(2016) paper, the set $\mathbf{M}(7^2)$ is completely determined.