  We pursue the study of the high energy behaviour of the gluon propagator on
the lattice in the Landau gauge in the flavorless case (n_f=0). It was shown in
a precedin g paper that the gluon propagator did not reach three-loop
asymptotic scaling at an energy scale as high as 5 GeV.
  Our present high statistics analysis includes also a simulation at
$\beta=6.8$ ($a\simeq 0.03$ fm), which allows to reach $\mu \simeq 10$ GeV.
Special care has been devoted to the finite lattice-spacing artifacts as well
as to the finite volume effects, the latter being acute at $\beta=6.8$ where
the volume is bounded by technical limits. Our main conclusion is a strong
evidence that the gluon propagator has reached three-loop asymptotic scaling,
at $\mu$ ranging from 5.6 GeV to 9.5 GeV. We buttress up this conclusion on
several demanding criteria of asymptoticity, including scheme independence. Our
fit in the 5.6 GeV to 9.5 GeV window yields $\Lambda^{\bar{{\rm MS}}} =
  319 \pm 14 ^{+10}_{-20}$ MeV, in good agreement with our previous result,
$\Lambda^{\bar{{\rm MS}}} = 295 \pm 20 $ MeV, obtained from the three gluon
vertex, but it is significantly above the Schr\"odinger functional method
estimate : $238 \pm 19$ MeV. The latter difference is not understood.
Confirming our previous paper, we show that a fourth loop is necessary to fit
the whole ($2.8 \div 9.5$) GeV energy window.
