The nature and origin of free-floating planets (FFPs) are still largely unconstrained because of a lack of large homogeneous samples to enable a statistical analysis of their properties. So far, most FFPs have been discovered using indirect methods; microlensing surveys have proved particularly successful to detect these objects down to a few Earth masses. However, the ephemeral nature of microlensing events prevents any follow-up observations and individual characterization. Several studies have identified FFPs in young stellar clusters and the Galactic field but their samples are small or heterogeneous in age and origin. Here we report the discovery of between 70 and 170 FFPs (depending on the assumed age) in the region encompassing Upper Scorpius and Ophiuchus, the closest young OB association to the Sun. We found an excess of FFPs by a factor of up to seven compared with core-collapse model predictions, demonstrating that other formation mechanisms may be at work. We estimate that ejection from planetary systems might have a contribution comparable to that of core collapse in the formation of FFPs. Therefore, ejections due to dynamical instabilities in giant exoplanet systems must be frequent within the first 10Myr of a system's life.