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Using a finite volume Gradient Flow (GF) renormalization scheme withSchr\"odinger Functional (SF) boundary conditions, we compute thenon-perturbative running coupling in the range $2.2 \lesssim {\barg}_\mathrm{GF}^2(L) \lesssim 13$. Careful continuum extrapolations turn out tobe crucial to reach our high accuracy. The running of the coupling is alwaysbetween one-loop and two-loop and very close to one-loop in the region of$200\,{\rm MeV} \lesssim \mu=1/L \lesssim 4\,{\rm GeV}$. While there is noconvincing contact to two-loop running, we match non-perturbatively to the SFcoupling with background field. In this case we know the $\mu$ dependence up to$\sim 100\,{\rm GeV}$ and can thus connect to the $\Lambda$-parameter.

Slow running of the Gradient Flow coupling from 200 MeV to 4 GeV in $N_{\rm f}=3$ QCD