Planar sets with few empty convex polygons
Adrian Dumitrescu · Studia Scientiarum Mathematicarum Hungarica · 2000
A configuration of n points in general position in the plane is described which has less than 1.684n² empty triangles, less than 2.132n² empty convex quadrilaterals, less than 1.229n² empty convex pentagons and less than 0.298n² empty convex hexagons. This improves the constants from a previous construction given by Valtr.