  The random q-state quantum Potts model is studied on hypercubic lattices in
dimensions 2 and 3 using the numerical implementation of the Strong Disorder
Renormalization Group introduced by Kovacs and Igl{\'o}i [Phys. Rev. B 82,
054437 (2010)]. Critical exponents $\nu$, d f and $\psi$ at the Infinite
Disorder Fixed Point are estimated by Finite-Size Scaling for several numbers
of states q between 2 and 50. When scaling corrections are not taken into
account, the estimates of both d f and $\psi$ systematically increase with q.
It is shown however that q-dependent scaling corrections are present and that
the exponents are compatible within error bars, or close to each other, when
these corrections are taking into account. This provides evidence of the
existence of a super-universality of all 2D and 3D random Potts models.
