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Now that {\it (i)} the uncertainty due to the Higgs boson mass dependence is no longer relevant; {\it (ii)} the uncertainty due to the top-quark mass dependence is negligible; and {\it (iii)} the pQCD scale uncertainty from the latest {\rm N_3LO} calculations~has dropped to 0.0002, this method potentially allows access to high precision on $\alpha_{\rm s}$. As shown in Eq.~\ref{eq:Rl}, $R_\ell$ was measured at LEP with a relative uncertainty is 0.12\%. This precision is expected to improve to better than $10^{-5}$ with TLEP. The LEP experimental error of 0.0028 on $\alpha_s (m^2_{\rm Z})$ will scale accordingly to better than 0.00015 at TLEP.\\  {\em A reasonable target for the measurement of $\alpha_s (m^2_{\rm Z})$ with a run at the Z pole with TLEP is therefore a precision of 0.00015.}  Beyond the measurement of $R_\ell$ at the Z pole, another interesting possibility for the $\alpha_{\rm s}$ determination is to use the W hadronic width as measured from W-pair events at and above 161 GeV. The quantity of interest is the branching ratio $B_{\rm had}= \Gamma_{\rm W \to hadrons}/\Gamma^tot_{\rm W}$, which can extract be extracted by measuring the fractions of WW events to the   fully leptonic, semi-leptonic and fully hadronic final states:   \begin{equation}   {\rm BR}({\rm W^+W^-} \to \ell^+ \nu \ell’^- \bar{\nu}) = (1-B_{\rm had})^2 \\   {\rm BR}({\rm W^+W^-} \to \ell^+ \nu {\rm q\bar{q}’}) = (1-B_{\rm had})\times B_{\rm had} \\   {\rm BR}({\rm W^+W^-} \to {\rm q\bar{q}' q’’\bar{q}’’’})= B_{\rm had}^2   \end{equation}       The LEP2 data taken at centre-of-mass energies ranging from 183 to 209 GeV led to $B_{\rm had} = 67.41 \pm 0.27$~\cite{1302.3415}, a measurement with a 0.4\% relative precision. This measurement that was limited by WW event statistics of about $4 × 10^4$ events. With over $2 \times 10^8 W$ pairs expected at TLEP at $\sqrt{s} =$ 161, 240 and 350~GeV, it may therefore be possible to reduce the relative uncertainty on $B_{\rm had}$ by a factor $\sim 70$ down to $5\times 10^{-5}$, and thus the absolute uncertainty on $\alpha_{\rm s}$ to $\pm 0.00015$.     This measurement is complementary that that performed with the Z hadronic width, because the sensitivity to electroweak effects is completely different in $B_{\rm had}$ and in $R_\ell$. In particular, the coupling of the W to pairs of quarks and leptons is straightforwardly given by the CKM matrix elements with little sensitivity to any new particles.     {\em A reasonable target for the measurement of $\alpha_s (m^2_{\rm W})$ with the runs at and above 161 GeV with TLEP is therefore a precision better than 0.0002. When combined with the measurement at Z pole, a precision of 0.0001 is within reach for $\alpha_s (m^2_{\rm Z})$.}