Abstract:
 A spherical twodistance set is a ?nite collection of unit vectors in R^n such that the set of distances between any two distinct vectors has cardinality two. O.R. Musin used Delsarte’s linear programming method to prove the result when 7 ? n ? 39, except n=23. We use the semide?nite programming and sum of square method (SOS) to compute improved estimates of the maximum size of spherical twodistance sets. Exact answers are found for dimensions n = 23 and 40 ? n ? 94, where previous results gave divergent bounds.
