Smallest Universal Set of Points for Planar Graphs

How many points must be placed in the plane to support planar drawing of all planar graphs on $n$ vertices? More precisely, call a set of points universal if every planar graph on $n$ vertices can be drawn with straight-line edges and without crossings by placing the vertices on a subset of the points. What is the smallest universal set of points as a function of $n$? In particular, is it $O(n)$?