A construction of spherical 3-designs

T. Miezaki

doi:10.37863/umzh.v74i1.986

T. Miezaki Waseda Univ., Tokyo, Japan

DOI: https://doi.org/10.37863/umzh.v74i1.986

Keywords: Spherical designs, Lattices, Spherical harmonics

Abstract

UDC 512.5

We give a construction for spherical 3-designs. This construction is a generalization of Bondarenko’s results.

References

A. V. Bondarenko, On a spherical code in the space of spherical harmonics, Ukr. Math. J., 62, № 6, 993 – 996 (2010), https://doi.org/10.1007/s11253-010-0407-6 DOI: https://doi.org/10.1007/s11253-010-0407-6

J. H. Conway, N. J. A. Sloane, Sphere packings lattices and groups, third ed., Springer, New York (1999), https://doi.org/10.1007/978-1-4757-6568-7 DOI: https://doi.org/10.1007/978-1-4757-6568-7

P. Delsarte, J.-M. Goethals, J. J. Seidel, Spherical codes and designs, Geom. Dedicata, 6, 363 – 388 (1977), https://doi.org/10.1007/bf03187604 DOI: https://doi.org/10.1007/BF03187604

G. Nebe, B. Venkov, The strongly perfect lattices of dimension 10, Colloque International de Theorie des Nombres (Talence, 1999), J. Theor. Nombres Bordeaux, 12, № 2, 503 – 518 (2000). DOI: https://doi.org/10.5802/jtnb.294

G. Nebe, B. Venkov, Low-dimensional strongly perfect lattices. I. The 12-dimensional case, Enseign. Math., 51, № 1-2, 129 – 163 (2005).

B. Venkov, Réseaux et designs sphériques. (French) Réseaux euclidiens, designs sphériques et formes modulaires, Monogr. Enseign. Math., 37, 10 – 86, (2001).