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On Euclidean designs and potential energy
The electronic journal of combinatorics, Tome 19 (2012) no. 1
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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.
DOI : 10.37236/8
Classification : 05B30, 31C20
Mots-clés : Euclidean \(a\)-code, lower bound on the cardinalities of Euclidean \(t\)-designs 
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     author = {Tsuyoshi Miezaki and Makoto Tagami},
     title = {On {Euclidean} designs and potential energy},
     journal = {The electronic journal of combinatorics},
     year = {2012},
     volume = {19},
     number = {1},
     doi = {10.37236/8},
     zbl = {1243.05054},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/8/}
}
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Tsuyoshi Miezaki; Makoto Tagami. On Euclidean designs and potential energy. The electronic journal of combinatorics, Tome 19 (2012) no. 1. doi: 10.37236/8

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