  We provide new examples of Cayley graphs on which the quantum walks reach
uniform mixing. Our first result is a complete characterization of all
$2(d+2)$-regular Cayley graphs over $\mathbb{Z}_3^d$ that admit uniform mixing
at time $2\pi/9$. Our second result shows that for every integer $k\ge 3$, we
can construct Cayley graphs over $\mathbb{Z}_q^d$ that admit uniform mixing at
time $2\pi/q^k$, where $q=3, 4$.
  We also find the first family of irregular graphs, the Cartesian powers of
the star $K_{1,3}$, that admit uniform mixing.
