Correlated sampling of halos from z = 6 to z = 30 within a 300 cMpc box. Top: total halo mass function within the box at from redshifts z = 6 to z = 30, compared to the Sheth-Tormen unconditional mass function represented as a shaded region with Poisson uncertainty. The black dotted line corresponds to a number density of one halo in the simulation volume within that bin. Bottom: ratio of the sampled mass function to the expected Sheth–Tormen unconditional mass function, showing an excess of small halos at the highest redshifts, but remaining within Poisson errors over the vast majority of masses and redshifts.