An energy scan near the $tau$ pair production threshold has been performed using the BESIII detector. About $24$ pb$^{-1}$ of data, distributed over four scan points, was collected. This analysis is based on $tau$ pair decays to $ee$, $emu$, $eh$, $mumu$, $mu h$, $hh$, $erho$, $murho$ and $pirho$ final states, where $h$ denotes a charged $pi$ or $K$. The mass of the $tau$ lepton is measured from a maximum likelihood fit to the $tau$ pair production cross section data to be $m_{tau} = (1776.91pm0.12 ^{+0.10}_{-0.13}$) MeV/$c^2$, which is currently the most precise value in a single measurement.
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