The Maximum Number of Bases in a Family of Vectors

David Ellis, Maria-Romina Ivan, Imre Leader

The proportion of $d$-element subsets of ${\mathbb{F}}_2^d$ that are bases is asymptotic to ${\prod }_{j=1}^{\infty }(1-2^{-j})\approx 0.29$ as $d\to \infty$. It is natural to ask whet…