  We 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 (3 Gpc/h) characterized by an unprecedented combination of
volume and mass resolution, down to 1.85x10^9 M_sun/h. 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 all the methods 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 a_par and a_perp to within 0.9%, and fsig8 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 Dark Energy Spectroscopic Instrument (DESI) galaxy
sample.
