  Precision tests of QCD perturbation theory are not readily available from
experimental data. The main reasons are systematic uncertainties due to the
confinement of quarks and gluons, as well as kinematical constraints which
limit the accessible energy scales. We here show how continuum extrapolated
lattice data may overcome such problems and provide excellent probes of
renormalized perturbation theory. This work corresponds to an essential step in
the ALPHA collaboration's project to determine the $\Lambda$-parameter in
3-flavour QCD. I explain the basic techniques used in the high energy regime,
namely the use of mass-independent renormalization schemes for the QCD coupling
constant in a finite Euclidean space time volume. When combined with finite
size techniques this allows one to iteratively step up the energy scale by
factors of 2, thereby quickly covering two orders of magnitude in scale. We may
then compare perturbation theory (with $\beta$-functions available up to 3-loop
order) to our non-perturbative data for a 1-parameter family of running
couplings. We conclude that a target precision of 3 percent for the
$\Lambda$-parameter requires non-perturbative data up to scales where
$\alpha_s\approx 0.1$, whereas the apparent precision obtained from applying
perturbation theory around $\alpha_s \approx 0.2$ can be misleading. This
should be taken as a general warning to practitioners of QCD perturbation
theory.
