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Geometriae Dedicata

, Volume 43, Issue 2, pp 167–179 | Cite as

Construction of spherical t-designs

  • Bela Bajnok
Article

Abstract

Spherical t-designs are Chebyshev-type averaging sets on the d-dimensional unit sphere Sd−1, that are exact for polynomials of degree at most t. The concept of such designs was introduced by Delsarte, Goethals and Seidel in 1977. The existence of spherical t-designs for every t and d was proved by Seymour and Zaslavsky in 1984. Although some sporadic examples are known, no general construction has been given. In this paper we give an explicit construction of spherical t-designs on Sd−1 containing N points, for every t,d and N,NN0, where N0 = C(d)t O(d 3).

Keywords

Unit Sphere Explicit Construction General Construction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Kluwer Academic Publishers 1992

Authors and Affiliations

  • Bela Bajnok
    • 1
  1. 1.Department of Applied MathematicsThe University of Houston-DowntownHoustonU.S.A.

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