  We study the flavorless gluon propagator in the Landau gauge from high
statistics lattice calculations. Hypercubic artifacts are efficiently
eliminated by taking the $\sum p_\mu^4 \to 0$ limit. The propagator is fitted
to the three-loops perturbative formula in an energy window ranging form $\sim$
2.5 GeV up to $\sim$ 5.5 GeV. $\alpha_s$ is extracted from the best fit in a
continuous set of renormalisation schemes. The fits are very good, with a
$\chi^2$ per d.o.f smaller than 1. We propose a more stringent test of
asymptotic scaling based on scheme independence of the resulting $\Lambda_{\bar
MS}$. This method shows that asymptotic scaling at three loops is not reached
by the gluon propagator although we use rather large energies. We are only able
to obtain an effective flavorless three-loops estimate $\Lambda_{\bar
MS}^{(3)}= 353 \pm 2 ^{+25}_{-10} $ MeV. We argue that the real asymptotic
value for $\Lambda_{\bar MS}$ should plausibly be smaller.
