  Almost perfect nonlinear (APN) functions play an important role in the design
of block ciphers as they offer the strongest resistance against differential
cryptanalysis. Despite more than 25 years of research, only a limited number of
APN functions are known. In this paper, we show that a recent construction by
Taniguchi provides at least $\frac{\varphi(m)}{2}\left\lceil \frac{2^m+1}{3m}
\right\rceil$ inequivalent APN functions on the finite field with ${2^{2m}}$
elements, where $\varphi$ denotes Euler's totient function. This is a great
improvement of previous results: for even $m$, the best known lower bound has
been $\frac{\varphi(m)}{2}\left(\lfloor \frac{m}{4}\rfloor +1\right)$, for odd
$m$, there has been no such lower bound at all. Moreover, we determine the
automorphism group of Taniguchi's APN functions.
