Let $M$ be a paving matroid with $m$ elements and rank $n$. Is there any lower bound for the number of bases of $M$? There is an upper bound for the number of hyperplanes (see [here][1], page 97) but since not all hyperplanes are $n$-subsets in paving matroids, it is not clear whether this upper bound is helpful to find a bound for the number of bases.


  [1]: https://pure.tue.nl/ws/files/75493302/20170920_Pol.pdf