  Generating pre-initial conditions (or particle loads) is the very first step
to set up a cosmological N-body simulation. In this work, we revisit the
numerical convergence of pre-initial conditions on dark matter halo properties
using a set of simulations which only differs in initial particle loads, i.e.
grid, glass, and the newly introduced capacity constrained Voronoi tessellation
(CCVT). We find that the median halo properties agree fairly well (i.e. within
a convergence level of a few per cent) among simulations running from different
initial loads. We also notice that for some individual haloes cross-matched
among different simulations, the relative difference of their properties
sometimes can be several tens of per cent. By looking at the evolution history
of these poorly converged haloes, we find that they are usually merging haloes
or haloes have experienced recent merger events, and their merging processes in
different simulations are out-of-sync, making the convergence of halo
properties become poor temporarily. We show that, comparing to the simulation
starting with an anisotropic grid load, the simulation with an isotropic CCVT
load converges slightly better to the simulation with a glass load, which is
also isotropic. Among simulations with different pre-initial conditions, haloes
in higher density environments tend to have their properties converged slightly
better. Our results confirm that CCVT loads behave as well as the widely used
grid and glass loads at small scales, and for the first time we quantify the
convergence of two independent isotropic particle loads (i.e. glass and CCVT)
on halo properties.
