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The ALPHA collaboration aims to determine $\alpha_s(m_Z)$ with a total errorbelow the percent level. A further step towards this goal can be taken bycombining results from the recent simulations of 2+1-flavour QCD by the CLSinitiative with a number of tools developed over the years: renormalizedcouplings in finite volume schemes, recursive finite size techniques, two-looprenormalized perturbation theory and the (improved) gradient flow on thelattice. We sketch the strategy, which involves both the standard SF couplingin the high energy regime and a gradient flow coupling at low energies. Thisimplies the need for matching both schemes at an intermediate switching scale,$L_{\rm swi}$, which we choose roughly in the range 2-4 GeV. In thiscontribution we present a preliminary result for this matching procedure, andwe then focus on our almost final results for the scale evolution of the SFcoupling from $L_{\rm swi}$ towards the perturbative regime, where we extractthe $N_{\rm f} = 3$ ${\Lambda}$-parameter, ${\Lambda}_{\overline{\rmMS}}^{N_{\rm f}=3}$, in units of $L_{\rm swi}$ . Connecting $L_{\rm swi}$ andthus the ${\Lambda}$-parameter to a hadronic scale such as $F_K$ requires 2further ingredients: first, the connection of $L_{\rm swi}$ to $L_{\rm max}$using a few steps with the step-scaling function of the gradient flow coupling,and, second, the continuum extrapolation of $L_{\rm max} F_K$.

A status update on the determination of ${\Lambda}_{\overline{\rm MS}}^{N_{\rm f}=3}$ by the ALPHA collaboration