  Three typical algorithms of Pauli blocking in the quantum molecular dynamics
type models are investigated in the nuclear matter, the nucleus and the heavy
ion collisions. The calculations in nuclear matter show that the blocking
ratios obtained with the three algorithms are underestimated 13-25\% compared
to the analytical values of blocking ratios. For the finite nucleus, the
spurious collisions occur around the surface of the nucleus owing to the
defects of Pauli blocking algorithms. In the simulations of heavy ion
collisions, the uncertainty of stopping power from different Pauli blocking
algorithms is less than 5\%. Furthermore, the in-medium effects of
nucleon-nucleon ($NN$) cross sections on the nuclear stopping power are
discussed. Our results show that the transport models calculations with free
$NN$ cross sections result in the stopping power decreasing with the beam
energy at the beam energy less than 300 MeV/u. To increase or decrease the
values of stopping power, an enhanced or suppressed model dependent in-medium
$NN$ cross section is required.
