  We show that for any prime odd integer $d$, there exists a correlation of
size $\Theta(r)$ that can robustly self-test a maximally entangled state of
dimension $4d-4$, where $r$ is the smallest multiplicative generator of
$\mathbb{Z}_d^\ast$. The construction of the correlation uses the embedding
procedure proposed by Slofstra (Forum of Mathematics, Pi. Vol. $7$, ($2019$)).
Since there are infinitely many prime numbers whose smallest multiplicative
generator is at most $5$ (M. Murty The Mathematical Intelligencer $10.4$
($1988$)), our result implies that constant-sized correlations are sufficient
for robust self-testing of maximally entangled states with unbounded local
dimension.
