  The effects of local inhomogeneities on low redshift $H_0$ determinations are
studied by estimating the redshift-distance relation of mock sources in N-body
simulations. The results are compared to those obtained using the standard
approach based on Hubble's law. The comparison shows a clear tendency for the
standard approach to yield lower values of $H_0$ than the approach based on the
scheme using light rays. The difference is, however, small. More precisely, it
is found that the overall effect of inhomogeneities on the determination of
$H_0$ is a small increase in the local estimates of about $0.3\%$ compared to
the results obtained with Hubble's law, when based on a typical distribution of
supernovae in the redshift range $0.01 < z < 0.1$. The overall conclusion of
the study is a verification of the results that have earlier been obtained by
using Hubble's law: The effects of inhomogeneities on local $H_0$ estimates are
not significant enough to make it plausible that differences in high- and
low-redshift estimates of $H_0$ are due to small inhomogeneities within the
setting of standard cosmology.
