We briefly summarize the outcomes of our recent improved fits to the experimental data of CCFR collaboration for $xF_3$ structure function of $ u N$ deep-inelastic scattering at the next-to-next-to-leading order. Special attention is paid to the extraction of $alpha_s(M_Z)$ and the parameter of the infrared renormalon model for $1/Q^2$-correction at different orders of perturbation theory. The results can be of interest for planning similar studies using possible future data of Neutrino Factories.
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