  In the previous paper, we established an elementary bound for numbers of
points of surfaces in the projective $3$-space over ${\Bbb F}_q$. In this
paper, we give the complete list of surfaces that attain the elementary bound.
Precisely those surfaces are the hyperbolic surface, the nonsingular Hermitian
surface, and the surface of minimum degree containing all ${\Bbb F}_q$-points
of the $3$-space.
