  For each nontrivial semisimple Hopf algebra $H$ of dimension sixteen over
$\mathbb{C}$, the smallest dimension inner-faithful representation of $H$
acting on a quadratic AS regular algebra $A$ of dimension 2 or 3, homogeneously
and preserving the grading, is determined. Each invariant subring $A^H$ is
determined. When $A^H$ is also AS regular, thus providing a generalization of
the Chevalley-Shephard-Todd Theorem, we say that $H$ is a reflection Hopf
algebra for $A$.
