  Current microlensing surveys are sensitive to free-floating planets down to
Earth-mass objects. All published microlensing events attributed to unbound
planets were identified based on their short timescale (below two days), but
lacked an angular Einstein radius measurement (and hence lacked a significant
constraint on the lens mass). Here, we present the discovery of a Neptune-mass
free-floating planet candidate in the ultrashort ($t_{\rm E}=0.320\pm0.003$
days) microlensing event OGLE-2016-BLG-1540. The event exhibited strong
finite-source effects, which allowed us to measure its angular Einstein radius
of $\theta_{\rm E}=9.2\pm0.5\,\mu$as. There remains, however, a degeneracy
between the lens mass and distance. The combination of the source proper motion
and source-lens relative proper motion measurements favors a Neptune-mass lens
located in the Galactic disk. However, we cannot rule out that the lens is a
Saturn-mass object belonging to the bulge population. We exclude stellar
companions up to 15 au.
