  The QCD free energy can be studied by dimensional reduction to a
three-dimensional (3d) effective theory, whereby non-perturbative lattice
simulations become less demanding. To connect to the original QCD a
perturbative matching computation is required, which is conventionally carried
out in dimensional regularization. Therefore the 3d lattice results need to be
converted to this regularization scheme as well. The conversion must be carried
up to 4-loop order, where the free energy displays an infrared (IR)
singularity. We therefore need a regulator which can be implemented both on the
lattice and in the continuum computation. We introduce a mass regulator to
perform Numerical Stochastic Perturbation Theory computations. Covariant gauge
is fixed in the Faddeev-Popov scheme without introducing any ghost fields.
