A new lower bound on the maximum number of plane graphs using production matrices

We use the concept of production matrices to show that there exist sets of $n$ points in the plane that admit $\mathrm{\Omega }({42.11}^n)$ crossing-free geometric graphs. This improves the previously best known bound of $\mathrm{\Omega }({41.18}^n)$ by Aichholzer et al. (2007).