  In this paper, we consider relational structures arising from Comer's finite
field construction, where the cosets need not be sum free. These Comer schemes
generalize the notion of a Ramsey scheme and may be of independent interest. As
an application, we give the first finite representation of $34_{65}$. This
leaves $33_{65}$ as the only remaining relation algebra in the family $N_{65}$
with a flexible atom that is not known to be finitely representable. Motivated
by this, we complement our upper bounds with some lower bounds. Using a SAT
solver, we show that $33_{65}$ is not finitely representable on fewer than $24$
points, and that $33_{65}$ does not admit a cyclic group representation on
fewer than $120$ points. We also employ a SAT solver to show that $34_{65}$ is
not representable on fewer than $24$ points.
