• DOI:10.1007/BF00147866
• Corpus ID: 118360818

Construction of spherical t-designs

@article{Bajnok1992ConstructionOS,
  title={Construction of spherical t-designs},
  author={B{\'e}la Bajnok},
  journal={Geometriae Dedicata},
  year={1992},
  volume={43},
  pages={167-179}
}

• B. Bajnok
• Published 1 August 1992
• Mathematics
• Geometriae Dedicata

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,N≥N0, where N0 = C(d)tO(d3).