  The $\Z_{p^s}$-additive codes of length $n$ are subgroups of $\Z_{p^s}^n$,
and can be seen as a generalization of linear codes over $\Z_2$, $\Z_4$, or
$\Z_{2^s}$ in general. A $\Z_{p^s}$-linear generalized Hadamard (GH) code is a
GH code over $\Z_p$ which is the image of a $\Z_{p^s}$-additive code by a
generalized Gray map. A partial classification of these codes by using the
dimension of the kernel is known. In this paper, we establish that some
$\Z_{p^s}$-linear GH codes of length $p^t$ are equivalent, once $t$ is fixed.
This allows us to improve the known upper bounds for the number of such
nonequivalent codes. Moreover, up to $t=10$, this new upper bound coincides
with a known lower bound (based on the rank and dimension of the kernel).
