  We present for the first time the inclusive cross section for associated
Higgs boson production with a massive gauge boson at
next-to-next-to-next-to-leading order in QCD. Furthermore, we introduce n3loxs,
a public, numerical program for the evaluation of inclusive cross sections at
the third order in the strong coupling constant. Our tool allows to derive
predictions for charged- and neutral-current Drell-Yan production, gluon- and
bottom-quark-fusion Higgs boson production and Higgs boson associated
production with a heavy gauge boson. We discuss perturbative and parton
distribution function (PDF) uncertainties of the aforementioned processes. We
perform a comparison of global PDF sets for a variety of process including
associated Higgs boson production and observe $1\sigma$ deviations among
predictions for several processes.
