  We present the UNIT $N$-body cosmological simulations project, designed to
provide precise predictions for nonlinear statistics of the galaxy
distribution. We focus on characterizing statistics relevant to emission line
and luminous red galaxies in the current and upcoming generation of galaxy
surveys. We use a suite of precise particle mesh simulations (FastPM) as well
as with full $N$-body calculations with a mass resolution of $\sim
1.2\times10^9\,h^{-1}$M$_{\odot}$ to investigate the recently suggested
technique of Angulo & Pontzen 2016 to suppress the variance of cosmological
simulations We study redshift space distortions, cosmic voids, higher order
statistics from $z=2$ down to $z=0$. We find that both two- and three-point
statistics are unbiased. Over the scales of interest for baryon acoustic
oscillations and redshift-space distortions, we find that the variance is
greatly reduced in the two-point statistics and in the cross correlation
between halos and cosmic voids, but is not reduced significantly for the
three-point statistics. We demonstrate that the accuracy of the two-point
correlation function for a galaxy survey with effective volume of 20
($h^{-1}$Gpc)$^3$ is improved by about a factor of 40, indicating that two
pairs of simulations with a volume of 1 ($h^{-1}$Gpc)$^3$ lead to the
equivalent variance of $\sim$150 such simulations. The $N$-body simulations
presented here thus provide an effective survey volume of about seven times the
effective survey volume of DESI or Euclid. The data from this project,
including dark matter fields, halo catalogues, and their clustering statistics,
are publicly available at http://www.unitsims.org.
