  Square coloring is a variant of graph coloring where vertices within distance
two must receive different colors. When considering planar graphs, the most
famous conjecture (Wegner, 1977) states that $\frac32\Delta+1$ colors are
sufficient to square color every planar graph of maximum degree $\Delta$. This
conjecture has been proven asymptotically for graphs with large maximum degree.
We consider here planar graphs with small maximum degree and show that
$2\Delta+7$ colors are sufficient, which improves the best known bounds when
$6\leqslant \Delta\leqslant 31$.
