  The structural and dynamic properties of the dark matter halos, though an
important ingredient in understanding large-scale structure formation, require
more conservative particle resolution than those required by halo mass alone in
a simulation. This reduces the parameter space of the simulations, more
severely for high-redshift and large-volume mocks which are required by the
next-generation large sky surveys. Here, we incorporate redshift and cosmology
dependence into an algorithm that assigns accurate halo properties such as
concentration, spin, velocity, and spatial distribution to the sub-resolution
haloes in a simulation. By focusing on getting the right correlations with halo
mass and local tidal anisotropy $\alpha$ measured at $4 \times$ halo radius,
our method will also recover the correlations of these small scale structural
properties with the large-scale environment, i.e., the halo assembly bias at
all scales greater than $5 \times$ halo radius. We find that the distribution
of halo properties is universal with redshift and cosmology. By applying the
algorithm to a large volume simulation $(600 h^{-1}{\rm Mpc})$, we can access
the $30-500$ particle haloes, thus gaining an order of magnitude in halo mass
and two to three orders of magnitude in number density at $z=2-4$. This
technique reduces the cost of mocks required for the estimation of covariance
matrices, weak lensing studies, or any large-scale clustering analysis with
less massive haloes.
