We give a new upper bound for the rectilinear crossing number cr(n) of the complete geometric graph Kn. We prove that cr(n) ≤ 0.380559 ¡n 4 ¢ + Θ(n3 ) by means of a new construction based on an iterative duplication strategy starting with a set having a certain structure of halving lines.
Bernardo M. Ábrego, Silvia Fernández