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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, 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.

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    $\begingroup$ A general version of this question had been asked a while ago. You may want to look at the answers and comments there. mathoverflow.net/q/212411/22051 $\endgroup$
    – Felix Goldberg
    Commented Apr 30, 2023 at 13:24

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