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- W1657506800 abstract "We study Euclidean designs from the viewpoint of the potential energy. For a finite set in Euclidean space, we formulate a linear programming bound for the potential energy by applying harmonic analysis on a sphere. We also introduce the concept of strong Euclidean designs from the viewpoint of the linear programming bound, and we give a Fisher type inequality for strong Euclidean designs. A finite set on Euclidean space is called a Euclidean $a$-code if any distinct two points in the set are separated at least by $a$. As a corollary of the linear programming bound, we give a method to determine an upper bound on the cardinalities of Euclidean $a$-codes on concentric spheres of given radii. Similarly we also give a method to determine a lower bound on the cardinalities of Euclidean $t$-designs as an analogue of the linear programming bound." @default.
- W1657506800 created "2016-06-24" @default.
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- W1657506800 date "2012-01-06" @default.
- W1657506800 modified "2023-09-28" @default.
- W1657506800 title "On Euclidean Designs and Potential Energy" @default.
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- W1657506800 doi "https://doi.org/10.37236/8" @default.
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