Geodesic
On the existence of minimum cubature formulas for Gaussian measure on $\mathbb R^{2}$ of degree $t$ supported by $[\frac{t}{4}]+1$ circles
Journal of Algebraic Combinatorics, Tome 35 (2012) no. 1, pp. 109-119.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this paper we prove that there exists no minimum cubature formula of degree $4 k$ and $4 k+2$ for Gaussian measure on $\Bbb R ^{2}$ supported by $k+1$ circles for any positive integer $k$, except for two formulas of degree 4.
Keywords: keywords cubature formula, Euclidean design, Gaussian design, Laguerre polynomial 
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     author = {Bannai, Eiichi and Bannai, Etsuko and Hirao, Masatake and Sawa, Masanori},
     title = {On the existence of minimum cubature formulas for {Gaussian} measure on $\mathbb R^{2}$ of degree $t$ supported by $[\frac{t}{4}]+1$ circles},
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     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2012__35_1_a3/}
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Bannai, Eiichi; Bannai, Etsuko; Hirao, Masatake; Sawa, Masanori. On the existence of minimum cubature formulas for Gaussian measure on $\mathbb R^{2}$ of degree $t$ supported by $[\frac{t}{4}]+1$ circles. Journal of Algebraic Combinatorics, Tome 35 (2012) no. 1, pp. 109-119. http://geodesic.mathdoc.fr/item/JAC_2012__35_1_a3/