Does anybody know if there is any research on a lower bound on the number of (non-isomorphic) unlabeled planar graphs with maximum node degree $d$?

Alternatively, a lower bound on the number of all unlabeled planar graphs will also help if the proof could possibly be modified for graphs with bounded degree. There is, for example, a paper by Giménez and Noy on the asymptotic number of labeled planar graphs but it seems not too easy to understand and modify the proof to work for unlabeled planar graphs with bounded degree.

I'm not looking for the best bounds known. Something like $\Omega(2^{cn})$ for some $c>0$ (preferably with an easier proof than the best known result) would be sufficient (if it holds).

Paper mentioned before:

- Giménez, Omer, and Marc Noy. "The number of planar graphs and properties of random planar graphs." International Conference on Analysis of Algorithms DMTCS proc. AD. Vol. 147. 2005.