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The ratio $ R_\ell$ of the partial width of the Z into hadrons to that to one massless charged-lepton flavour has been used for the determination of $\alpha_s$ at LEP. As shown in Eq.~\ref{eq:Rl}, $R_\ell$ was measured at LEP with a relative uncertainty is 0.12\%. Up to a few years ago, when only NNLO QCD predictions were available, and the Higgs boson mass was still unknown, this measurement was translated to~\cite{Bethke_2004}  \begin{equation}  \small  \alpha_{\rm s} (m^2_{\rm Z}) &  = 0.1226 \pm 0.0038 \ ({\rm exp}) {\ }^{+0.0028\ (\mu = 2.00 m_{\rm Z})}_{−0.0005\ (\mu = 0.25 m_{\rm Z})} {\ }^{+0.0033\ (m_{\rm H} = 900\ {\rm GeV}/c^2)}_{−0.0000\ (m_{\rm H} = 100\ {\rm GeV}/c^2)}  {\ }^{+0.0002\ (m_{\rm top} = 180 {\rm GeV}/c^2)}_{-0.0002\ (m_{\rm top} = 170 {\rm GeV}/c^2)} \pm 0.0002\ ({\rm renormal. \ schemes}) th}) \\   &  = 0.1226^{+0.0058}_{−0.0038} \end{equation}  Since the uncertainty due to the Higgs mass dependence is no longer relevant, the top quark mass dependence is negligible, and the pQCD scale uncertainty from latest NNNLO calculations [6, 7] is only 0.0002 on $\alpha_s (M^2_Z)$, this method should allow access to high precision on $\alpha_s$.