Spherical t-design with d=(t+1)^2 points

Found by Xiaojun Chen and Rob Womersley


Table 1


Computed spherical designs Y
Error to the exact spherical designs Y*

||Y-Y*||_infty< = r


Determinant of the interpolation matrix G(Y)
Extremal(maximum determinant) points Y0

||Y-Y0||_infty< = r0




Image Spherical 16-design with 289 points
t d points Y error r logdetG(Y) r0
2 9 P2_9 1.01e-15-3.21570.0510
3 16 P3_162.36e-152.57790.5484
4 25 P4_251.80e-1415.93370.2004
5 36 P5_361.34e-1435.48290.5190
649 P6_49 3.45e-1462.64430.3636
7 64 P7_645.07e-14100.41670.2554
8 81 P8_811.15e-13144.36110.5548
9 100 P9_1001.84e-13186.22650.5052
10121 P10_121 6.14e-11265.50510.0716
11 144 P11_1441.82e-13341.67790.0370
12 169 P12_1691.43e-12427.41530.0346
13 196 P13_1962.43e-11524.27900.0526
14 225 P14_225 5.55e-11632.71540.0470
15 256 P15_256 3.08e-11752.47700.0182
16 289 P16_256 4.60e-11884.33550.0199
17 324 P17_324 4.38e-111028.08640.0294
18 361 P18_361 2.26e-101184.33070.0285

Extremal Points (Rob Womersley home page ).