  We investigate which planar point sets allow simultaneous straight-line
embeddings of all planar graphs on a fixed number of vertices. We first show
that $(1.293-o(1))n$ points are required to find a straight-line drawing of
each $n$-vertex planar graph (vertices are drawn as the given points); this
improves the previous best constant $1.235$ by Kurowski (2004).
  Our second main result is based on exhaustive computer search: We show that
no set of 11 points exists, on which all planar 11-vertex graphs can be
simultaneously drawn plane straight-line. This strengthens the result by
Cardinal, Hoffmann, and Kusters (2015), that all planar graphs on $n \le 10$
vertices can be simultaneously drawn on particular `universal' sets of $n$
points while there are no universal sets for $n \ge 15$. Moreover, we provide a
set of 49 planar 11-vertex graphs which cannot be simultaneously drawn on any
set of 11 points. This, in fact, is another step towards a (negative) answer of
the question, whether every two planar graphs can be drawn simultaneously -- a
question raised by Brass, Cenek, Duncan, Efrat, Erten, Ismailescu, Kobourov,
Lubiw, and Mitchell (2007).
