  We study the convex combinations of the $(d+1)$ generalized Pauli dynamical
maps in a Hilbert space of dimension $d$. For certain choices of the
decoherence function, the maps are noninvertible and they remain under convex
combinations as well. For the case of dynamical maps characterized by the
decoherence function $(1-e^{-ct})/n$ with the decoherence parameter $n$ and
decay factor $c$, we evaluate the fraction of invertible maps obtained upon
mixing, which is found to increase superexponentially with dimension $d$.
