Sphere-packings, lattices, and groups
Sphere-packings, lattices, and groups
Necessary conditions for existence of some designs in polynomial metric spaces
European Journal of Combinatorics
Spherical Designs and Generalized Sum-Free Sets in AbelianGroups
Designs, Codes and Cryptography
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
A method for proving nonexistence of spherical designs of odd strength and odd cardinality
Problems of Information Transmission
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We investigate the structure of spherical 驴-designs by applying polynomial techniques for investigation of some inner products of such designs. Our approach can be used for large variety of parameters (dimension, cardinality, strength). We obtain new upper bounds for the largest inner product, lower bounds for the smallest inner product and some other bounds. Applications are shown for proving nonexistence results either in small dimensions and in certain asymptotic process. In particular, we complete the classification of the cardinalities for which 3-designs on $${\mathbb{S}^{n-1}}$$ exist for n = 8, 13, 14 and 18. We also obtain new asymptotic lower bound on the minimum possible odd cardinality of 3-designs.