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We present an update on Numerical Stochastic Perturbation Theory projects forLattice QCD, which are by now run on apeNEXT. As a first issue, we discuss astrategy to tackle finite size effects which can be quite sizeable in thecomputation of logarithmically divergent renormalization constants. Our firsthigh loop determination of quark bilinears for Wilson fermions was limited tofinite constants and finite ratios. A precise determination of Z_P and Z_S (andhence of Z_m) now becomes possible. We also give an account of computations foractions different from the standard regularization we have taken into accountso far (Wilson gauge action and Wilson fermions). In particular, we present thestatus of computations for the Lattice QCD regularization defined by tree levelSymanzik improved gauge action and Wilson fermions, which became quite popularin recent times. We also take the chance to discuss the related topic of thecomputation of the gluon and ghost propagators (which we undertook incollaboration with another group). This is relevant in order to betterunderstand non-perturbative computations of propagators aiming atqualitative/quantitative understanding of confinement.

High loop renormalization constants by NSPT: a status report