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SubHalo Abundance Matching (SHAM) is an empirical method for constructinggalaxy catalogues based on high-resolution $N$-body simulations. We apply SHAMon the UNIT simulation to simulate SDSS BOSS/eBOSS Luminous Red Galaxies (LRGs)within a wide redshift range of $0.2 < z < 1.0$. Besides the typical SHAMscatter parameter $\sigma$, we include $v_{\rm smear}$ and $V_{\rm ceil}$ totake into account the redshift uncertainty and the galaxy incompletenessrespectively. These two additional parameters are critical for reproducing theobserved 2PCF multipoles on 5--25$\,h^{-1}\,{\rm Mpc}$. The redshiftuncertainties obtained from the best-fitting $v_{\rm smear}$ agree with thosemeasured from repeat observations for all SDSS LRGs except for the LOWZ sample.We explore several potential systematics but none of them can explain thediscrepancy found in LOWZ. Our explanation is that the LOWZ galaxies mightcontain another type of galaxies which needs to be treated differently. Theevolution of the measured $\sigma$ and $V_{\rm ceil}$ also reveals that theincompleteness of eBOSS galaxies decreases with the redshift. This is theconsequence of the magnitude lower limit applied in eBOSS LRG target selection.Our SHAM also set upper limits for the intrinsic scatter of the galaxy--halorelation given a complete galaxy sample: $\sigma_{\rm int}<0.31$ for LOWZ at$0.2<z<0.33$, $\sigma_{\rm int}<0.36$ for LOWZ at $0.33<z<0.43$, and$\sigma_{\rm int}<0.46$ for CMASS at $0.43<z<0.51$. The projected 2PCFs of ourSHAM galaxies also agree with the observational ones on the 2PCF fitting range.

Model BOSS & eBOSS Luminous Red Galaxies at 0.2 < z < 1.0 using SubHalo Abundance Matching with 3 parameters