  We present two large cosmological N-body simulations, called Horizon Run 2
(HR2) and Horizon Run 3 (HR3), made using 6000^3 = 216 billions and 7210^3 =
374 billion particles, spanning a volume of (7.200 Gpc/h)^3 and (10.815
Gpc/h)^3, respectively. These simulations improve on our previous Horizon Run 1
(HR1) up to a factor of 4.4 in volume, and range from 2600 to over 8800 times
the volume of the Millennium Run. In addition, they achieve a considerably
finer mass resolution, down to 1.25x10^11 M_sun/h, allowing to resolve
galaxy-size halos with mean particle separations of 1.2 Mpc/h and 1.5 Mpc/h,
respectively. We have measured the power spectrum, correlation function, mass
function and basic halo properties with percent level accuracy, and verified
that they correctly reproduce the LCDM theoretical expectations, in excellent
agreement with linear perturbation theory. Our unprecedentedly large-volume
N-body simulations can be used for a variety of studies in cosmology and
astrophysics, ranging from large-scale structure topology, baryon acoustic
oscillations, dark energy and the characterization of the expansion history of
the Universe, till galaxy formation science - in connection with the new
SDSS-III. To this end, we made a total of 35 all-sky mock surveys along the
past light cone out to z=0.7 (8 from the HR2 and 27 from the HR3), to simulate
the BOSS geometry. The simulations and mock surveys are already publicly
available at http://astro.kias.re.kr/Horizon-Run23/.
