  We investigate using three-point statistics in constraining the galaxy-halo
connection. We show that for some galaxy samples, the constraints on the halo
occupation distribution parameters are dominated by the three-point function
signal (over its two-point counterpart). We demonstrate this on mock catalogs
corresponding to the Luminous Red Galaxies (LRGs), Emission-Line Galaxies
(ELG), and quasars (QSOs) targeted by the Dark Energy Spectroscopic Instrument
(DESI) Survey. The projected three-point function for triangle sides less up to
20$h^{-1}$ Mpc measured from a cubic Gpc of data can constrain the
characteristic minimum mass of the LRGs with a precision of $0.46$ %. For
comparison, similar constraints from the projected two-point function are
$1.55$ %. The improvements for the ELGs and QSOs targets are more modest. In
the case of the QSOs it is caused by the high shot-noise of the sample, and in
the case of the ELGs, this is caused by the range of halo masses of the host
halos. The most time-consuming part of our pipeline is the measurement of the
three-point functions. We adopt a tabulation method, proposed in earlier works
for the two-point function, to reduce significantly the required compute time
for the three-point analysis.
