  For graphs of bounded maximum average degree, we consider the problem of
2-distance coloring. This is the problem of coloring the vertices while
ensuring that two vertices that are adjacent or have a common neighbor receive
different colors. It is already known that planar graphs of girth at least 6
and of maximum degree D are list 2-distance (D+2)-colorable when D>=24 (Borodin
and Ivanova (2009)) and 2-distance (D+2)-colorable when D>=18 (Borodin and
Ivanova (2009)). We prove here that D>=17 suffices in both cases. More
generally, we show that graphs with maximum average degree less than 3 and
D>=17 are list 2-distance (D+2)-colorable. The proof can be transposed to list
injective (D+1)-coloring.
