Planet formation theories predict that some planets may be ejected from their parent systems as result of dynamical interactions and other processes(1-3). Unbound planets can also be formed through gravitational collapse, in a way similar to that in which stars form(4). A handful of free-floating planetary-mass objects have been discovered by infrared surveys of young stellar clusters and star-forming regions(5,6) as well as wide-field surveys(7), but these studies are incomplete(8-10) for objects below five Jupiter masses. Gravitational microlensing is the only method capable of exploring the entire population of free-floating planets down to Mars-mass objects, because the microlensing signal does not depend on the brightness of the lensing object. A characteristic timescale of microlensing events depends on the mass of the lens: the less massive the lens, the shorter the microlensing event. A previous analysis(11) of 474 microlensing events found an excess of ten very short events (1-2 days)-more than known stellar populations would suggest-indicating the existence of a large population of unbound or wide-orbit Jupiter-mass planets (reported to be almost twice as common as main-sequence stars). These results, however, do not match predictions of planet-formation theories(3,12) and surveys of young clusters(8-10). Here we analyse a sample of microlensing events six times larger than that of ref. 11 discovered during the years 2010-15. Although our survey has very high sensitivity (detection efficiency) to short-timescale (1-2 days) microlensing events, we found no excess of events with timescales in this range, with a 95 per cent upper limit on the frequency of Jupiter-mass free-floating or wide-orbit planets of 0.25 planets per main-sequence star. We detected a few possible ultrashort-timescale events (with timescales of less than half a day), which may indicate the existence of Earth-mass and super-Earth-mass free-floating planets, as predicted by planet-formation theories(3,12).