It is known that for all finite n ≥ 5, there are relation algebras with n-dimensional relational bases but no weak representations. We prove that conversely, there are finite weakly representable relation algebras with no n-dimensional relational bases. In symbols: neither of the classes RAn and wRRA contains the other.
"Weak representations of relation algebras and relational bases." J. Symbolic Logic 76 (3) 870 - 882, September 2011. https://doi.org/10.2178/jsl/1309952524