The article “On the constant D(q) defined by Homma” by the algebra group members Peter Beelen, Maria Montanucci, and Lara Vicino has been accepted for publication in the Proceedings of the 18th Conference on Arithmetic, Geometry, Cryptography, and Coding Theory in the AMS book series Contemporary Mathematics (CONM). In this article, we investigate the asymptotic behaviour of the number of points on an algebraic curve defined over a finite field in relation to its degree. A preprint of this article can be found here.