Content deleted Content added
m →Football pools problem: improved appearence |
Added bounds for ternary covering codes K3(n,2) and K3(n,3) |
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Line 31:
If <math>n=\tfrac12 (3^k-1)</math> then 3<sup>''n''-''k''</sup> are needed, so for ''n'' = 4, ''k'' = 2, 9 are needed; for ''n'' = 13, ''k'' = 3, 59049 are needed.<ref>http://alexandria.tue.nl/repository/freearticles/593454.pdf</ref> The best bounds known as of 2011<ref>http://www.sztaki.hu/~keri/codes/3_tables.pdf</ref> are
{| class="wikitable" style="text-align:center;"
! ''n''
! | 1
Line 63:
| '''59049'''
| 166610-177147
|-
! ''K''<sub>3</sub>(''n'',2)
|
| '''1'''
| '''3'''
| '''3'''
| '''8'''
|15-17
| 26-34
| 54-81
| 130-219
| 323-555
| '''729'''
| 1919-2187
| 5062-6561
| 12204-19683
|-
! ''K''<sub>3</sub>(''n'',3)
|
|
| '''1'''
| '''3'''
| '''3'''
| '''6'''
| 11-12
| 14-27
| 27-54
| 57-105
| 117-243
| 282-657
| 612-1215
| 1553-2187
|}
| |||