Chebyshev-type quadrature on multidimensional domains
Journal of Approximation Theory
Polynomial techniques for investigation of spherical designs
Designs, Codes and Cryptography
A method for proving nonexistence of spherical designs of odd strength and odd cardinality
Problems of Information Transmission
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We extend the concepts of sum-freesets and Sidon-sets of combinatorial number theory with the aimto provide explicit constructions for spherical designs. We calla subset S of the (additive) abelian group G t-free if for all non-negative integers kand l with k+l \leq t, the sum of k(not necessarily distinct) elements of S does notequal the sum of l (not necessarily distinct) elementsof S unless k=l and the two sums containthe same terms. Here we shall give asymptotic bounds for thesize of a largest t-free set in \small{{ Z}}_n,and for t \leq 3 discuss how t-freesets in \small{{ Z}}_n can be used to constructspherical t-designs.