Construction of sphericalt-designs

✍ Scribed by Bela Bajnok

• Publisher: Springer
• Year: 1992
• Tongue: English
• Weight: 463 KB
• Volume: 43
• Category: Article
• ISSN: 0046-5755
• DOI: 10.1007/bf00147866

✦ Synopsis

Spherical t-designs are Chebyshev-type averaging sets on the d-dimensional unit sphere S d-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 S ~-~ containing N points, for every t, d and N, N ~> No, where N O = C(d)t O(d3).