Editing Kissing number (section)

==Some known bounds==

The following table lists some known bounds on the kissing number in various dimensions.<ref name=Machado>{{cite journal|last1=Machado|first1=Fabrício C.|last2=Oliveira|first2=Fernando M.|title=Improving the Semidefinite Programming Bound for the Kissing Number by Exploiting Polynomial Symmetry|year=2018|pages=362–369|volume=27|journal=[[Experimental Mathematics (journal)|Experimental Mathematics]]|issue=3|arxiv=1609.05167|doi=10.1080/10586458.2017.1286273|s2cid=52903026}}</ref> The dimensions in which the kissing number is known are listed in boldface.

[[File:Kissing growth.svg|thumb|right|upright=1.5|Rough volume estimates show that kissing number in ''n'' dimensions [[Exponential growth|grows exponentially]] in ''n''. The base of exponential growth is not known. The grey area in the above plot represents the possible values between known upper and lower bounds.  Circles represent values that are known exactly.]]
{| class="wikitable" style="text-align: center; margin-left: 40pt;"
!Dimension
!Lower<br>bound
!Upper<br>bound
|-
|'''1''' 
|colspan=2 | 2 
|-
|'''2'''
|colspan=2 | [[A2 lattice|6]]
|-
|'''3'''
|colspan=2 | [[A3 lattice|12]]
|-
|'''4'''  
|colspan=2 | [[D4 lattice|24]]<ref name="Musin"/> 
|-
|5  
|[[D5 lattice|40]]
|44
|-
|6  
|[[E6 lattice|72]]
|77
|-
|7  
|[[E7 lattice|126]]
|134
|-
|'''8'''
|colspan=2 | [[E8 lattice|240]]
|-
|9
|306 
|363
|-
|10
|510
|553
|-
|11
|593<ref>https://storage.googleapis.com/deepmind-media/DeepMind.com/Blog/alphaevolve-a-gemini-powered-coding-agent-for-designing-advanced-algorithms/AlphaEvolve.pdf</ref>
|868
|-
|12
|840
|1,355
|-
|13
|1,154
|2,064
|-
|14
|1,932
|3,174
|-
|15
|2,564
|4,853
|-
|16
|4,320
|7,320
|-
|17
|5,730
|10,978
|-
|18
|7,654
|16,406
|-
|19
|11,692
|24,417
|-
|20
|19,448
|36,195
|-
|21
|29,768
|53,524
|-
|22
|49,896
|80,810
|-
|23
|93,150
|122,351
|-
|'''24'''
|colspan=2 | [[Leech lattice|196,560]]
|}