  We calculate shear viscosity and bulk viscosity in SU(3) gauge theory on the
lattice at $1.5 \,T_c$. The viscosities are extracted via a Kubo formula from
the reconstructed spectral function which we determine from the Euclidean-time
dependence of the corresponding channel of the energy-momentum tensor
correlators. We obtain unprecedented precision for the correlators by applying
gradient flow and blocking methods. The correlators are extrapolated to the
continuum and then to zero flow time. To extract the viscosities we fit
theoretically inspired models to the lattice data and crosscheck the fit
results using the Backus Gilbert method. The final estimates for shear and bulk
viscosity are $\eta/s = 0.15-0.48$ and $\zeta/s = 0.017-0.059$.
