  A measurement of the top quark mass is performed using a data sample enriched
with single top quark events produced in the $t$ channel. The study is based on
proton-proton collision data, corresponding to an integrated luminosity of 35.9
fb$^{-1}$, recorded at $\sqrt{s}$ = 13 TeV by the CMS experiment at the LHC in
2016. Candidate events are selected by requiring an isolated high-momentum
lepton (muon or electron) and exactly two jets, of which one is identified as
originating from a bottom quark. Multivariate discriminants are designed to
separate the signal from the background. Optimized thresholds are placed on the
discriminant outputs to obtain an event sample with high signal purity. The top
quark mass is found to be 172.13 $^{+0.76}_{-0.77}$ GeV, where the uncertainty
includes both the statistical and systematic components, reaching sub-GeV
precision for the first time in this event topology. The masses of the top
quark and antiquark are also determined separately using the lepton charge in
the final state, from which the mass ratio and difference are determined to be
0.9952 $^{+0.0079}_{-0.0104}$ and 0.83 $^{+1.79}_{-1.35}$ GeV, respectively.
The results are consistent with $CPT$ invariance.
