Table 1. Riesz energy ratios for the five orientation sampling sets of Fig. 3.
Each set contains 2 × 106 samples (both q and −q are included in the Riesz summations). The first row shows the actual energies E s for the optimal sampling. The ratios r s are equal to unity for the optimal sampling.
| Sampling | r 1 (E 1) | r 2 (E 2) | r 3 (E 3) |
|---|---|---|---|
| Optimal | 3 395 305 452 627.101 | 4 000 000 000 000.000 | 12 315 331 182 477.914 |
|
1.007 179 463 867 | 1.052 447 214 340 | 2.966 778 018 561 |
|
1.011 244 456 259 | 1.051 526 042 008 | 2.474 120 685 576 |
|
0.999 999 863 775 | 1.000 006 692 433 | 1.969 498 539 602 |
|
0.999 946 255 258 | 0.993 015 676 166 | 1.019 190 812 726 |
|
0.999 957 141 142 | 0.994 310 813 958 | 1.063 893 792 814 |