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.
Categories: math.CO