Lower bound on the number of faces of a polyhedron of genus g

Example of polyhedron with 4096 faces and 4097 holes.

P. McMullen, C. Schulz, and J.M. Wills. "Polyhedral manifolds in E3 with unusually large genus". Israel Journal of Mathematics., 46 (1983), no. 1-2, pages 127–144

https://link.springer.com/article/10.1007%2FBF02760627