Let $\mathbb F=GF(2)$. I would like to estimate the cardinality of the automorphism group of $\mathbb F^n$ as function of $n$. I know that it must be lower than $2^{n^2}$, but is there a way to provide an exact value (or at least a lower bound)?
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1$Aut(\Bbb F^n)\cong GL_n(\Bbb F)$, and there is a formula for its cardinality, for $GF(q)$. – Dietrich Burde Jan 02 '25 at 15:24