  We study {0,\alpha}-sets, which are sets of unit vectors of $\mathbb{C}^m$ in
which any two distinct vectors have angle 0 or \alpha. We investigate some
distance-regular graphs that provide new constructions of {0,\alpha}-sets using
a method by Godsil and Roy. We prove bounds for the sizes of {0,\alpha}-sets of
flat vectors, and characterize all the distance-regular graphs that yield
{0,\alpha}-sets meeting the bounds at equality.
