New upper bound for spherical two-distance sets from semi-definite programming.
Abstract:
A spherical two-distance set is a finitecollection of unit vectors inR^nsuch that the set of distances betweenany two distinct vectors has cardinality two. O.R. Musinused Delsarte’slinearprogramming method to prove the result when 7≤ n ≤ 39, exceptn=23. We use the semi-definiteprogramming and sum of square method(SOS)tocompute improved estimates of the maximum size of spherical two-distancesets. Exact answers are found for dimensions n = 23 and 40 ≤ n ≤ 94, whereprevious results gave divergent bounds.
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