The theory of SQS and guidelines for generating these structures are given in this papers A. Zunger, S.-H. Wei, L. Ferreira, J.E. Bernard, Special quasirandom structures, Phys. Rev. Lett. 65 (3) (1990) 353; S.-H. Wei, L. G. Ferreira, James E. Bernard, and Alex Zunger, Phys. Rev. B 42, 9622 (1990), see also
https://docs.quantumatk.com/manual/Types/EvolutionarySQS/EvolutionarySQS.html.
As a general guideline, increasing accuracy of SQS requires larger supercells, higher Max Expansion Order (the current default is likely good enough so), using larger number of generations, using the largest possible cluster diameter, see a png-file enclosed. The goal is to get error for correlation functions as small as possible for a given expansion order and max cluster diameters (default is likely good enough). Note that setting very strict parameters might lead to significant increase of computational time. Again, quality of SQS is quantified in terms of correlation function errors.
