We report the results of a deep near-infrared (JHK) survey of the outer parts of the Trapezium Cluster with Gemini South/Flamingos. 396 sources were detected in a 26-arcmin^2^ area, including 138 brown dwarf candidates, defined as M<0.075M_{sun}_ for an assumed age of 1Myr. Only 33 of the brown dwarf candidates are planetary mass candidates with estimated masses in the range 0.003<M<0.012M_{sun}_. In an extinction-limited sample (AV<5) complete to approximately 0.005M_{sun}_ (5M_Jup_) the mass function appears to drop by a factor of 2 at the deuterium burning threshold, i.e. at planetary masses. After allowing for background contamination it is likely that planetary mass objects at 3-13M_Jup_ number <10% of the cluster population, with an upper limit of 13%. Analysis of the spatial distribution of stars and brown dwarf candidates suggests that brown dwarfs and very low-mass stars (M<0.1M_{sun}_) are less likely than more massive stars to have wide (>150AU) binary companions.