for $z<0.14$, the C4 catalog is $>90\%$ complete, with $<10\%$ contamination, for halos of ${\rm M_{200}} > 10^{14}{\rm M_{\odot}}$.

### Mass Estimator and Dynamic Range: Challenges Three and Four {#mass}

![The relation between the dark matter halo mass in our simulation and the total summed $r$ luminosity. The line is the best fit and the scatter, for a given mass, is $<30$%.[]{data-label="matchesLr"}](matchesLr.ps){width="7cm"}

In Figure \[matchesLr\], I present the correlation between the ${\rm
M_{200}}$ dark matter halo mass (taken directly from Evrard et al. 2002) and the total summed $r$ band luminosities for 4734 clusters that match in the HV simulation. As expected, these two quantities are linearly correlated over 2 orders of magnitude in both the halo mass and optical luminosity. The measured scatter for the whole dataset is $25\%$ (measured perpendicular to the best fit line). This plot demonstrates that we have address the 3$^{rd}$ and 4$^{th}$ challenges in Section \[algorithms\].

In the future, the C4 algorithm will be extended to include: [*i)*]{} Higher resolution dark matter simulations to test the sensitivity of the algorithm to lower mass systems; [*ii)*]{} A range of cosmological simulations to probe our sensitivity to various cosmological parameters [*e.g.*]{}, $\sigma_8$; and [*iii)*]{} Improve our 