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We present a systematic search for optical counterparts to 13 gravitationalwave (GW) triggers involving at least one neutron star during LIGO/Virgo'sthird observing run. We searched binary neutron star (BNS) and neutron starblack hole (NSBH) merger localizations with the Zwicky Transient Facility (ZTF)and undertook follow-up with the Global Relay of Observatories WatchingTransients Happen (GROWTH) collaboration. The GW triggers had a medianlocalization of 4480 deg^2, median distance of 267 Mpc and false alarm ratesranging from 1.5 to 1e-25 per yr. The ZTF coverage had a median enclosedprobability of 39%, median depth of 20.8mag, and median response time of 1.5hr. The O3 follow-up by the GROWTH team comprised 340 UVOIR photometric points,64 OIR spectra, and 3 radio. We find no promising kilonova(radioactivity-powered counterpart) and we convert the upper limits toconstrain the underlying kilonova luminosity function. Assuming that allkilonovae are at least as luminous as GW170817 at discovery (-16.1mag), wecalculate our joint probability of detecting zero kilonovae is only 4.2%. If weassume that all kilonovae are brighter than -16.6mag (extrapolated peakmagnitude of GW170817) and fade at 1 mag/day (similar to GW170817), the jointprobability of zero detections is 7%. If we separate the NSBH and BNSpopulations, the joint probability of zero detections, assuming all kilonovaeare brighter than -16.6mag, is 9.7% for NSBH and 7.9% for BNS mergers.Moreover, <57% (<89%) of putative kilonovae could be brighter than -16.6magassuming flat (fading) evolution, at 90% confidence. If we further account forthe online terrestrial probability for each GW trigger, we find that <68% ofputative kilonovae could be brighter than -16.6mag. Comparing to model grids,we find that some kilonovae must have Mej < 0.03 Msun or Xlan>1e-4 or phi>30degto be consistent with our limits. (Abridged)

Kilonova Luminosity Function Constraints based on Zwicky Transient Facility Searches for 13 Neutron Star Mergers