Nonexistence of Certain Spherical Designs of Odd Strengths and Cardinalities

A spherical -design on Sn-1 is a finite set such that, for all polynomials f of degree at most , the average of f over the set is equal to the average of f over the sphere Sn-1 . In this paper we obtain some necessary conditions for the existence of designs of odd strengths and cardinalities. This gives nonexistence results in many cases. Asymptotically, we derive a bound which is better than the corresponding estimation ensured by the Delsarte-GoethalsSeidel bound. We consider in detail the strengths = 3 and = 5 and obtain further nonexistence results in these cases. When the nonexistence argument does not work, we obtain bounds on the minimum distance of such designs.

• Type: Journal
• Year: 1999
• Where: DCG
• Authors: Peter Boyvalenkov, Danyo Danev, Svetla Nikova
• Keywords: DCG 1999, Necessary Conditions, Nonexistence, Sphere Sn-1