Abstract
We extend the computations from our previous work to determine the maximum number of rational points on a curve over and with fixed gonality and small genus. We find, for example, that there is no curve of genus 5 and gonality 6 over a finite field. We propose two conjectures based on our data. First, an optimal curve of genus g has gonality at most . Second, an optimal curve of gonality γ and large genus over has rational points.
Correction Statement
This article has been republished with minor changes. These changes do not impact the academic content of the article.
Declaration of Interest
No potential conflict of interest was reported by the authors.