  The production cross section of 30.92 GeV/$c$ protons on carbon is measured
by the NA61/SHINE spectrometer at the CERN SPS by means of beam attenuation in
a copy (replica) of the 90-cm-long target of the T2K neutrino oscillation
experiment. The employed method for direct production cross-section estimation
minimizes model corrections for elastic and quasi-elastic interactions. The
obtained production cross section is
$\sigma_\mathrm{prod}~=~227.6~\pm~0.8\mathrm{(stat)}~_{-~3.2}^{+~1.9}\mathrm{(sys)}~{-~0.8}\mathrm{(mod)}$
mb. It is in agreement with previous NA61/SHINE results obtained with a thin
carbon target, while providing improved precision with a total fractional
uncertainty of less than 2$\%$. This direct measurement is performed to reduce
the uncertainty on the T2K neutrino flux prediction associated with the
re-weighting of the interaction rate of neutrino-yielding hadrons.
