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A parametrization of the lattice spacing ($a$) in terms of the bare coupling($\beta$) for the SU(3) Yang--Mills theory with the Wilson gauge action isgiven in a wide range of~$\beta$. The Yang--Mills gradient flow with respect tothe flow time~$t$ for the dimensionless observable, $t\frac{d}{dt}t^2\langleE(t)\rangle$, is utilized to determine the parametrization. With fine latticespacings ($6.3\le\beta\le7.5$) and large lattice volumes ($N_{\rms}=64$--$128$), the discretization and finite-volume errors are significantlyreduced to the same level as the statistical error.

Determination of Reference Scales for Wilson Gauge Action from Yang--Mills Gradient Flow