An experimental study of the O16(e,e′K+)NΛ16 reaction has been performed at Jefferson Lab. A thin film of falling water was used as a target. This permitted a simultaneous measurement of the p(e,e′K+)Λ, Σ0 exclusive reactions and a precise calibration of the energy scale. A ground-state binding energy of 13.76±0.16MeV was obtained for NΛ16 with better precision than previous measurements on the mirror hypernucleus OΛ16. Precise energies have been determined for peaks arising from a Λ in s and p orbits coupled to the p1/2 and p3/2 hole states of the N15 core nucleus.