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We briefly summarize the outcomes of our recent improved fits to the experimental data of CCFR collaboration for structure function of $\nu N$ deep-inelastic scattering at the next-to-next-to-leading order. Special attention is paid to the extraction of and the parameter of the infrared renormalon model for -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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