  Reconfigurable intelligent surfaces (RISs) consisting of multiple reflective
elements are a promising technique to enhance communication quality as they can
create favorable propagation conditions. In this letter, we characterize the
fundamental relations between the number of reflective elements and the system
sum-rate in RIS-assisted multi-user communications. It is known from previous
works that the received signal-to-noise ratio~(SNR) can linearly increase with
the squared number of RIS reflective elements, but how many elements are
sufficient to provide an acceptable system sum-rate still remains an open
problem. To this end, we derive the asymptotic capacity with zero-forcing (ZF)
precoding, and then discuss how many reflective elements are required so that
the ratio of the system sum-rate to the capacity can exceed a predefined
threshold. Numerical results verify our analysis.
