Lower bounds for spherical designs
Izvestiya. Mathematics , Tome 61 (1997) no. 3, pp. 673-683.

Voir la notice de l'article provenant de la source Math-Net.Ru

A new lower bound is obtained for the cardinality of spherical designs. In its dependence on dimension it improves the well-known bound of Delsarte by an exponential factor as the degree of the design tends to infinity.
@article{IM2_1997_61_3_a8,
     author = {V. A. Yudin},
     title = {Lower bounds for spherical designs},
     journal = {Izvestiya. Mathematics },
     pages = {673--683},
     publisher = {mathdoc},
     volume = {61},
     number = {3},
     year = {1997},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1997_61_3_a8/}
}
TY  - JOUR
AU  - V. A. Yudin
TI  - Lower bounds for spherical designs
JO  - Izvestiya. Mathematics 
PY  - 1997
SP  - 673
EP  - 683
VL  - 61
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1997_61_3_a8/
LA  - en
ID  - IM2_1997_61_3_a8
ER  - 
%0 Journal Article
%A V. A. Yudin
%T Lower bounds for spherical designs
%J Izvestiya. Mathematics 
%D 1997
%P 673-683
%V 61
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1997_61_3_a8/
%G en
%F IM2_1997_61_3_a8
V. A. Yudin. Lower bounds for spherical designs. Izvestiya. Mathematics , Tome 61 (1997) no. 3, pp. 673-683. http://geodesic.mathdoc.fr/item/IM2_1997_61_3_a8/

[1] Konvei Dzh., Sloen N., Upakovka sharov, reshetki gruppy, T. 1, 2, Mir, M., 1990

[2] Resnick B., Sums of even powers of real linear forms, Memoirs of the Amer. Math. Soc., 96, no. 463, 1992 | MR

[3] Seidel J., “Isometric embeddings and geometric designs”, Discrete Math., 136 (1994), 281–293 | DOI | MR | Zbl

[4] Sidelnikov V. M., “Ob ekstremalnykh mnogochlenakh, ispolzuemykh pri otsenkakh moschnosti koda”, Probl. peredachi inform., 16:3 (1980), 17–30 | MR | Zbl

[5] Levenshtein V. I., “O granitsakh dlya upakovok v $n$-mernom evklidovom prostranstve”, DAN SSSR, 245:6 (1979), 1299–1303 | MR

[6] Levenshtein V. I., “Granitsy dlya upakovok metricheskikh prostranstv i nekotorye ikh prilozheniya”, Problemy kibernetiki, 40 (1983), 43–110 | MR

[7] Chernykh N. I., “O nailuchshem priblizhenii periodicheskikh funktsii trigonometricheskimi polinomami v $L_2$”, Matem. zametki, 2:5 (1967), 513–522 | MR

[8] Yudin V. A., “Mnogomernaya teorema Dzheksona v $L_2$”, Matem. zametki, 29:9 (1981), 309–315 | MR | Zbl

[9] Delsarte P., Goethals J. M., Seidel J. J., “Spherical codes and design”, Geom. Dedicata, 6 (1977), 363–388 | MR | Zbl

[10] Boyvalenkov P., “Extremal Polynomials for obtaining Bounds for Spherical Codes and Designs”, Discrete Comput. Geom., 14 (1995), 167–183 | DOI | MR | Zbl

[11] Sege G., Ortogonalnye mnogochleny, Fizmatgiz, M., 1962

[12] Kurant R., Gilbert D., Metody matematicheskoi fiziki, T. 1, Gostekhizdat, L., 1951

[13] Sobolev S. L., Vvedenie v teoriyu kubaturnykh formul, Nauka, M., 1974 | MR

[14] Hardin R. H., Sloane N. J. A., “New spherical $4$-designs”, Discrete Math., 106/107 (1992), 255–264 | DOI | MR | Zbl

[15] Stein I., Veis G., Vvedenie v garmonicheskii analiz na evklidovykh prostranstvakh, Mir, M., 1974 | Zbl