  We improve the existing calculations of deep inelastic scattering to next to
next to leading order in the following manner. First, we use the recently
calculated values of the anomalous dimensions for moments with index n=10,12 in
ep scattering. Second, we use also recently calculated anomalous dimensions for
n=1,3,...,13 for xF3 in neutrino N scattering, to extend the calculation to
this process. Lastly, we use the determinantal constraints on the moments that
follow from positivity of the structure functions to stabilize the fits. We
find substantial improvement over previous results, getting the following
numbers: Lambda(n_f=4, 3 loops)= 274 \pm 20 MeV, alpha_s^{3
loops}(M_Z^2)=0.1166 \pm 0.0013 and chi^2/dof= 92/(153-18) from ep and, from
\nu N, Lambda(n_f=4, 3 loops)=255 \pm 72 MeV, alpha_s^{3 loops}(M_Z^2)=0.1153
\pm 0.0063 and chi^2/dof=0.335/(64-7). The errors take into account
experimental errors and higher twist effects among other estimated theoretical
errors. We can also extrapolate the fit, made originally for the range 3.5 <
Q^2 < 230 GeV^2 to higher momenta, obtaining very good reproduction of
experimental data up to Q^2=5000 GeV^2. From this, in particular, we can
exclude supersymmetric partners (squarks or gluinos) for masses up to some 60
GeV. The fitted value of the coupling is now, including the data at high Q^2,
alpha_s^{3 loops}(M_Z^2)=0.1163 \pm 0.0014.
