On a number of rational points on a plane curve of low degree

In Homma and Kim (2010), an upper bound of the number of rational points on a plane curve of degree d over Fq is found. Some examples attaining the bound are given in Homma and Kim (2010), whose degrees are q+2, q+1, q, q−1, q−1 (when q is a square), and 2. In this paper, we consider an actual upper bound on such numbers for curves of low degree for q≤7. Also we give explicit examples of curves attaining the sharp bound for each d and q.