We pursue the study of the high energy behavior of the gluon propagator on
the lattice in the Landau gauge in the flavorless case (n(f) = 0) It was Sh
own in a preceding paper that the gluon propagator did not reach three-loop
asymptotic scaling at an energy scale as high as 5 GeV. Our present high s
tatistics analysis includes also a simulation at beta = 6.8 (a similar or e
qual to 0.03 fm), which allows us to reach mu similar or equal to 10 GeV. S
pecial care has been devoted to the finite lattice-spacing artifacts as wel
l as to the finite-volume effects, the latter being acute at beta = 6.8 whe
re the volume is bounded by technical limits. Our main conclusion is strong
evidence that the gluon propagator has reached three-loop asymptotic scali
ng, at mu ranging from 5.6-9.5 GeV. We buttress up this conclusion on sever
al demanding criteria of asymptoticity, including scheme independence. Our
fit in the 5.6 GeV to 9.5 GeV window yields Lambda<(MS)over bar> = 319 +/-
14(-20)(+10) MeV, in good agreement with our previous result Lambda(<(MS)ov
er bar>) = 295 +/- 20 MeV, obtained from the three-gluon vertex, but it is
significantly above the Schrodinger functional method estimate: 238 +/- 19
MeV. The latter difference is not understood. Confirming our previous paper
, we show that a fourth loop is necessary to fit the whole (2.8-9.5) GeV en
ergy window.