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We present a novel approach to the construction of mock galaxy catalogues forlarge-scale structure analysis based on the distribution of dark matter halosobtained with effective bias models at the field level. We aim to produce mockgalaxy catalogues capable of generating accurate covariance matrices for anumber of cosmological probes that are expected to be measured in current andforthcoming galaxy redshift surveys (e.g. two- and three-point statistics). Weuse the bias assignment method (BAM) to model the statistics of halodistribution through a learning algorithm using a few detailed $N$-bodysimulations, and approximated gravity solvers based on Lagrangian perturbationtheory. Using specific models of halo occupation distributions, we generategalaxy mocks with the expected number density and central-satellite fraction ofemission-line galaxies, which are a key target of the DESI experiment. BAMgenerates mock catalogues with per cent accuracy in a number of summarystatistics, such as the abundance, the two- and three-point statistics of halodistributions, both in real and redshift space. In particular, the mock galaxycatalogues display $\sim 3\%-10\%$ accuracy in the multipoles of the powerspectrum up to scales of $k\sim 0.4\,h^{-1}{\rm Mpc}$. We show that covariancematrices of two- and three-point statistics obtained with BAM display a similarstructure to the reference simulation. BAM offers an efficient way to producemock halo catalogues with accurate two- and three-point statistics, and is ableto generate a variety of multi-tracer catalogues with precise covariancematrices of several cosmological probes. We discuss future developments of thealgorithm towards mock production in DESI and other galaxy-redshift surveys.(Abridged)

DESI Mock Challenge: Halo and galaxy catalogs with the bias assignment method