Context. We present a novel approach to the construction of mock galaxy catalogues for large-scale structure analysis based on the distribution of dark matter halos obtained with effective bias models at the field level. Aims. We aim to produce mock galaxy catalogues capable of generating accurate covariance matrices for a number of cosmological probes that are expected to be measured in current and forthcoming galaxy redshift surveys (e.g. two- and three-point statistics). The construction of the catalogues shown in this paper is part of a mock-comparison project within the Dark Energy Spectroscopic Instrument (DESI) collaboration.

Methods. We use the bias assignment method (BAM) to model the statistics of halo distribution through a learning algorithm using a few detailed N-body simulations, and approximated gravity solvers based on Lagrangian perturbation theory. We introduce cosmic-web-dependent corrections to modelling redshift-space distortions at the N-body level - both in the halo and galaxy distributions -, as well as a multi-scale approach for accurate assignment of halo properties. Using specific models of halo occupation distributions to populate halos, we generate galaxy mocks with the expected number density and central-satellite fraction of emission-line galaxies, which are a key target of the DESI experiment.

Results. BAM generates mock catalogues with per cent accuracy in a number of summary statistics, such as the abundance, the twoand three-point statistics of halo distributions, both in real and redshift space. In particular, the mock galaxy catalogues display similar to 3%-10% accuracy in the multipoles of the power spectrum up to scales of k similar to 0.4 h(-1)Mpc. We show that covariance matrices of two- and three-point statistics obtained with BAM display a similar structure to the reference simulation.

Conclusions. BAM o ffers an efficient way to produce mock halo catalogues with accurate two- and three-point statistics, and is able to generate a variety of multi-tracer catalogues with precise covariance matrices of several cosmological probes. We discuss future developments of the algorithm towards mock production in DESI and other galaxy-redshift surveys.