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We explore a possibility of optimization of the method of determination ofthe top quark mass from $M_{b\ell}$ distribution in semi-leptonic decays $t \tob \ell\nu$ at LHC and a future linear collider (LC). We discover that thesystematic and statistical errors of $M_t$ determination can be diminished ifconsidering the high moments over the distribution. In the case of LHC thisallows one to reduce more than in twice the errors, and in the case of LC toapproach to the precision expected at studying the threshold scan of the totalcross-section $e^+e^- \to t\bar t$.Comment: 15 pages, 6 figures; theoretical uncertainties are discussed in more  detail, three references are added, in formula (3) a parametrization is  change

Towards precision determination of the top-quark massfrom $\mathbf M_{b\ell}$ distribution in semi-leptonic decays