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Lower bounds for spherical designs. (English. Russian original) Zbl 0890.05015

Izv. Math. 61, No. 3, 673-683 (1997); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 61, No. 3, 213-223 (1997).
The author obtains a new lower bound for the cardinality of spherical designs. In its dependence on dimension it improves the well-known bound of Delsarte by an exponential factor as the degree of the design tends to infinity.
Reviewer: R.N.Mohan (Nuzvid)

MSC:

05B30 Other designs, configurations
65D32 Numerical quadrature and cubature formulas
05B40 Combinatorial aspects of packing and covering
94B99 Theory of error-correcting codes and error-detecting codes
33C65 Appell, Horn and Lauricella functions
52C17 Packing and covering in \(n\) dimensions (aspects of discrete geometry)
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