Sets of complex unit vectors with few inner products and distance-regular graphs

We study {0,α}{0,α}-sets, which are sets of unit vectors of CmCm in which the inner product of any two distinct vectors has absolute value 0 or α. We investigate some distance-regular graphs that provide new constructions of {0,α}{0,α}-sets using a method by Godsil and Roy. We prove bounds for the sizes of {0,α}{0,α}-sets of flat vectors, and characterize all the distance-regular graphs that yield {0,α}{0,α}-sets meeting the bounds at equality.