  In this paper, we establish a lower bound on the total number of inequivalent
APN functions on the finite field with $2^{2m}$ elements, where $m$ is even. We
obtain this result by proving that the APN functions introduced by Pott and the
second author, that depend on three parameters $k$, $s$ and $\alpha$, are
pairwise inequivalent for distinct choices of the parameters $k$ and $s$.
Moreover, we determine the automorphism group of these APN functions.
