  A measurement of the $t$-channel single-top-quark and single-top-antiquark
production cross-sections in the lepton+je ts channel is presented, using 3.2
fb$^{-1}$ of proton--proton collision data at a centre-of-mass energy of 13
TeV, recorded with the ATLAS detector at the LHC in 2015. Events are selected
by requiring one charged lepton (electron or muon), missing transverse
momentum, and two jets with high transverse momentum, exactly one of which is
required to be $b$-tagged. Using a binned maximum-likelihood fit to the
discriminant distribution of a neural network, the cross-sections are
determined to be $\sigma(tq) = 156 \pm 5 \, (\mathrm{stat.}) \pm 27 \,
(\mathrm{syst.}) \pm 3\,(\mathrm{lumi.})$ pb for single top-quark production
and $\sigma(\bar{t}q) = 91 \pm 4 \, (\mathrm{stat.}) \pm 18 \, (\mathrm{syst.})
\pm 2\,(\mathrm{lumi.})$ pb for single top-antiquark production, assuming a
top-quark mass of 172.5 GeV. The cross-section ratio is measured to be $R_t =
\sigma(tq)/\sigma(\bar{t}q) = 1.72 \pm 0.09 \, (\mathrm{stat.}) \pm 0.18 \,
(\mathrm{syst.})$.
