Geometriae Dedicata

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

Construction of spherical t-designs

  • Bela Bajnok


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).


Unit Sphere Explicit Construction General Construction 
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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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