  We present an extensive study of the effects of neutrino transport in
3-dimensional general relativistic radiation hydrodynamics (GRHD) simulations
of binary neutron star (BNS) mergers using our moment-based, energy-integrated
neutrino radiation transport (M1) scheme. We consider a total of 8 BNS
configurations, while varying equation of state models, mass ratios and grid
resolutions, for a total of 16 simulations. We find that M1 neutrino transport
is crucial in modeling the local absorption of neutrinos and the deposition of
lepton number throughout the medium. We provide an in-depth look at the effects
of neutrinos on the fluid dynamics and luminosity during the late inspiral and
post-merger phases, the properties of ejecta and outflow, and the post-merger
nucleosynthesis. The simulations presented in this work comprise an extensive
study of the combined effect of the equation of state and M1 neutrino transport
in GRHD simulations of BNS mergers, and establish that the solution provided by
our M1 scheme is robust across system properties and provides insight into the
effects of neutrino trapping in BNS mergers.
