The Completed SDSS-IV Extended Baryon Oscillation Spectroscopic Survey: N-body mock challenge for galaxy clustering measurements

35 pages, 16 figures, 12 tables. Submitted to MNRAS. A description of eBOSS and links to all associated publications can be found here: https://www.sdss.org/surveys/eboss/International audienceWe develop a series of N-body data challenges, functional to the final analysis of the extended Baryon Oscillation Spectroscopic Survey (eBOSS) Data Release 16 (DR16) galaxy sample. The challenges are primarily based on high-fidelity catalogs constructed from the Outer Rim simulation - a large box size realization ($3h^{-1}$Gpc) characterized by an unprecedented mass resolution, down to 1.85 x 10$^9h^{-1}$$M_\odot$. We generate synthetic galaxy mocks by populating Outer Rim halos with a variety of halo occupation distribution (HOD) schemes of increasing complexity, spanning different redshift intervals. We then assess the performance of three complementary redshift space distortion (RSD) models in configuration and Fourier space, adopted for the analysis of the complete DR16 eBOSS sample of Luminous Red Galaxies (LRGs). We find that all the methods are mutually consistent, with comparable systematic errors on the Alcock-Paczynski parameters and the growth of structure, and robust to different HOD prescriptions - thus validating the robustness of the models and the pipelines used for the baryon acoustic oscillation (BAO) and full shape clustering analysis. In particular, all the techniques are able to recover $\alpha_{II}$ and $\alpha_\bot$ to within 0.9%, and $f\sigma8$ to within 1.5%. As a by-product of our work, we are also able to gain interesting insights on the galaxy-halo connection. Our study is relevant for the final eBOSS DR16 `consensus cosmology', as the systematic error budget is informed by testing the results of analyses against these high-resolution mocks. In addition, it is also useful for future large-volume surveys, since similar mock-making techniques and systematic corrections can be readily extended to model for instance the DESI galaxy sample