List your company
ResearchFormerly WizWand

Sphere Kissing Problem on Sphere Kissing Problem

238,350Lower Bound K(n, α)PackingStar
-9,451.8454,881.33119,214.5183,547.67Nov 17, 2025
Updated 5mo ago

Evaluation results

MethodLinks
PackingStarn=31, α=1/2, New construction form / cosine set=K(7, 1/2) + K(24, 1/2) + 2\sum_{i=1}^{42} |Si|2025.11238,350
Previous best known [18]n=31, α=1/22025.11232,874
PackingStarn=30, α=1/2, New construction form / cosine set=K(6, 1/2) + K(24, 1/2) + 2\sum_{i=1}^{24} |Si|2025.11220,440
Previous best known [18]n=30, α=1/22025.11219,984
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|2025.11209,496
Previous best known [18]n=29, α=1/22025.11208,272
PackingStarn=28, α=1/2, New construction form / cosine set=K(4, 1/2) + K(24, 1/2) + 2\sum_{i=1}^8 |Si|2025.11204,520
Previous best known [18]n=28, α=1/22025.11204,368
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|2025.11200,044
Previous best known [18]n=27, α=1/22025.11199,976
PackingStarn=26, α=1/2, New construction form / cosine set=K(2, 1/2) + K(24, 1/2) + 2|S1| + 2|S2|2025.11198,550
Previous best known [18]n=26, α=1/22025.11198,512
PackingStarn=25, α=1/2, New construction form / cosine set=K(24, 1/2) + |S1|2025.11197,056
Previous best known [18]n=25, α=1/22025.11197,048
PackingStarn=78, α=1/4, New construction form / cosine set={−1/2, −5/16, −1/8, 1/16, 1/4}2025.11142,155
PackingStarn=13, α=1/2, New construction form / cosine set={−1, −1/2, −1/4, 0, 1/4, 1/2}2025.111,146
Previous best known [16]n=13, α=1/22025.111,130
PackingStarn=18, α=1/3, New construction form / cosine set={−1, 0, ±1/3}2025.11704
Previous best known [24]n=18, α=1/32025.11672
PackingStarn=17, α=1/3, New construction form / cosine set={−1, −7/9, −5/9, ±1/9, ±1/3}2025.11578
PackingStarn=21, α=1/4, New construction form / cosine set={−1/2, −1/8, 1/4}2025.11567
Previous best known [25]n=21, α=1/42025.11554
Previous best known [24]n=17, α=1/32025.11546
PackingStarn=20, α=1/4, New construction form / cosine set={−1/2, −1/8, 1/4}2025.11405
Previous best known [24]n=20, α=1/42025.11378
PackingStarn=22, α=1/5, New construction form / cosine set={−1, −1/5, 1/5}2025.11352
Previous best known [24]n=22, α=1/52025.11338
PackingStarn=14, α=1/3, New construction form / cosine set={−1, 0, ±1/3}2025.11252
Previous best known [23]n=14, α=1/32025.11240
PackingStarn=12, α=1/4, New construction form / cosine set={−1/2, −1/8, 1/4}2025.1181
Previous best known [22]n=12, α=1/42025.1179