  We introduce the Lomonosov suite of high-resolution N-body cosmological
simulations covering a full box of size 32 $h^{-1}$ Mpc with low-mass
resolution particles ($2\times10^7$ $h^{-1}\,M_\odot$) and three zoom-in
simulations of overdense, underdense and mean density regions at much higher
particle resolution ($4\times10^4$ $h^{-1}\,M_\odot$). The main purpose of this
simulation suite is to extend the concentration-mass relation of dark matter
halos down to masses below those typically available in large cosmological
simulations. The three different density regions available at higher resolution
provide a better understanding of the effect of the local environment on halo
concentration, known to be potentially important for small simulation boxes and
small halo masses. Yet, we find the correction to be small in comparison with
the scatter of halo concentrations. We conclude that zoom simulations, despite
their limited representativity of the volume of the Universe, can be
effectively used for the measurement of halo concentrations at least at the
halo masses probed by our simulations. In any case, after a precise
characterization of this effect, we develop a robust technique to extrapolate
the concentration values found in zoom simulations to larger volumes with
greater accuracy. All together, Lomonosov provides a measure of the
concentration-mass relation in the halo mass range $10^7-10^{10}$
$h^{-1}\,M_\odot$ with superb halo statistics. This work represents a first
important step to measure halo concentrations at intermediate, yet vastly
unexplored halo mass scales, down to the smallest ones. All Lomonosov data and
files are public for community's use.
