Sphere Kissing Problem on Sphere Kissing Problem
238,350Lower Bound K(n, α)PackingStar
Evaluation Results
| Method | Links | |
|---|---|---|
| PackingStarn=31, α=1/2, New construction form / cosine set=K(7, 1/2) + K(24, 1/2) + 2\sum_{i=1}^{42} |Si|2025.11 | 238,350 | |
| Previous best known [18]n=31, α=1/22025.11 | 232,874 | |
| PackingStarn=30, α=1/2, New construction form / cosine set=K(6, 1/2) + K(24, 1/2) + 2\sum_{i=1}^{24} |Si|2025.11 | 220,440 | |
| Previous best known [18]n=30, α=1/22025.11 | 219,984 | |
| PackingStarn=29, α=1/2, New construction form / cosine set=K(5, 1/2) + K(24, 1/2) + 2\sum_{i=1}^{12} |Si| + \sum_{i=13}^{14} |Si|2025.11 | 209,496 | |
| Previous best known [18]n=29, α=1/22025.11 | 208,272 | |
| PackingStarn=28, α=1/2, New construction form / cosine set=K(4, 1/2) + K(24, 1/2) + 2\sum_{i=1}^8 |Si|2025.11 | 204,520 | |
| Previous best known [18]n=28, α=1/22025.11 | 204,368 | |
| PackingStarn=27, α=1/2, New construction form / cosine set=K(3, 1/2) + K(24, 1/2) + 2|S1| + 2|S2| + \sum_{i=3}^5 |Si|2025.11 | 200,044 | |
| Previous best known [18]n=27, α=1/22025.11 | 199,976 | |
| PackingStarn=26, α=1/2, New construction form / cosine set=K(2, 1/2) + K(24, 1/2) + 2|S1| + 2|S2|2025.11 | 198,550 | |
| Previous best known [18]n=26, α=1/22025.11 | 198,512 | |
| PackingStarn=25, α=1/2, New construction form / cosine set=K(24, 1/2) + |S1|2025.11 | 197,056 | |
| Previous best known [18]n=25, α=1/22025.11 | 197,048 | |
| PackingStarn=78, α=1/4, New construction form / cosine set={−1/2, −5/16, −1/8, 1/16, 1/4}2025.11 | 142,155 | |
| PackingStarn=13, α=1/2, New construction form / cosine set={−1, −1/2, −1/4, 0, 1/4, 1/2}2025.11 | 1,146 | |
| Previous best known [16]n=13, α=1/22025.11 | 1,130 | |
| PackingStarn=18, α=1/3, New construction form / cosine set={−1, 0, ±1/3}2025.11 | 704 | |
| Previous best known [24]n=18, α=1/32025.11 | 672 | |
| PackingStarn=17, α=1/3, New construction form / cosine set={−1, −7/9, −5/9, ±1/9, ±1/3}2025.11 | 578 | |
| PackingStarn=21, α=1/4, New construction form / cosine set={−1/2, −1/8, 1/4}2025.11 | 567 | |
| Previous best known [25]n=21, α=1/42025.11 | 554 | |
| Previous best known [24]n=17, α=1/32025.11 | 546 | |
| PackingStarn=20, α=1/4, New construction form / cosine set={−1/2, −1/8, 1/4}2025.11 | 405 | |
| Previous best known [24]n=20, α=1/42025.11 | 378 | |
| PackingStarn=22, α=1/5, New construction form / cosine set={−1, −1/5, 1/5}2025.11 | 352 | |
| Previous best known [24]n=22, α=1/52025.11 | 338 | |
| PackingStarn=14, α=1/3, New construction form / cosine set={−1, 0, ±1/3}2025.11 | 252 | |
| Previous best known [23]n=14, α=1/32025.11 | 240 | |
| PackingStarn=12, α=1/4, New construction form / cosine set={−1/2, −1/8, 1/4}2025.11 | 81 | |
| Previous best known [22]n=12, α=1/42025.11 | 79 |