Finite representations for two small relation algebras

In this note, we give two different proofs that relation algebra ${52}_{65}$ is representable over a finite set. The first is probabilistic, and uses Johnson schemes. The second is an explicit group representation over $(\mathbb{Z}\mathrm{/}2\mathbb{Z}{)}^{10}$. We also give a finite representation of ${59}_{65}$ over $\mathbb{Z}\mathrm{/}113\mathbb{Z}$ using a technique due to Comer.