On the inductive McKay--Navarro condition for ${\mathsf{B}}_2(2^f)$ and ${\mathsf{G}}_2(3^f)$

We verify the inductive McKay–Navarro condition for the groups ${\mathsf{B}}_2(2^f)$ and ${\mathsf{G}}_2(3^f)$ and all primes if $f$ is odd. Further, we show that the equivariance part of the inductive condition holds for all integers $f$.