  A search is performed for the production of high-mass resonances decaying
into a photon and a jet in 3.2 fb$^{-1}$ of proton--proton collisions at a
centre-of-mass energy of $\sqrt{s} = 13$ TeV collected by the ATLAS detector at
the Large Hadron Collider. Selected events have an isolated photon and a jet,
each with transverse momentum above 150 GeV. No significant deviation of the
$\gamma+$jet invariant mass distribution from the background-only hypothesis is
found. Limits are set at 95% confidence level on the cross sections of generic
Gaussian-shaped signals and of a few benchmark phenomena beyond the Standard
Model: excited quarks with vector-like couplings to the Standard Model
particles, and non-thermal quantum black holes in two models of extra spatial
dimensions. The minimum excluded visible cross sections for Gaussian-shaped
resonances with width-to-mass ratios of 2% decrease from about 6 fb for a mass
of 1.5 TeV to about 0.8 fb for a mass of 5 TeV. The minimum excluded visible
cross sections for Gaussian-shaped resonances with width-to-mass ratios of 15%
decrease from about 50 fb for a mass of 1.5 TeV to about 1.0 fb for a mass of 5
TeV. Excited quarks are excluded below masses of 4.4 TeV, and non-thermal
quantum black holes are excluded below masses of 3.8 (6.2) TeV for
Randall--Sundrum (Arkani-Hamed--Dimopoulous--Dvali) models with one (six) extra
dimensions.
