  Thanks to dimensional reduction, the contributions to the hot QCD pressure
coming from so-called soft modes can be studied via an effective
three-dimensional theory named Electrostatic QCD (spatial Yang-Mills fields
plus an adjoint Higgs scalar). The poor convergence of the perturbative series
within EQCD suggests to perform lattice measurements of some of the associated
gluon condensates. These turn out, however, to be plagued by large
discretization artifacts. We discuss how Numerical Stochastic Perturbation
Theory can be exploited to determine the full lattice spacing dependence of one
of these condensates up to 4-loop order, and sharpen our tools on a concrete
2-loop example.
