Fragments of plane filling curves of degree $q+2$ over the finite field of $q$ elements, and of affine-plane filling curves of degree $q+1$

Masaaki Homma

Nonsingular plane curves over a finite field ${\mathbb{F}}_q$ of degree $q+2$ passing through all the ${\mathbb{F}}_q$-points of the plane admita representation by $3\times 3$ matrices…