Covering code: Difference between revisions

Revision as of 12:29, 28 October 2012

Revision as of 21:18, 28 October 2012

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== Football pools problem ==

A particular case is the '''football pools problem''', based on [[football pool]] betting, where the aim is to predict the results of <math>''n</math>'' football matches as a home win, draw or away win, or to at least predict <math>{{nowrap|''n'' - 1</math>}} of them with multiple bets. So this looks forThus a trinaryternary covering, ''K''<mathsub>3</sub>K_3(''n'',1)</math>, is sought.

If <math>n=\tfrac12 (3^k-1)</math> then 3<mathsup>3^{''n''-''k}''</mathsup> are needed, so for <math>''n'' = 4, ''k'' = 2</math>, 9 are needed; for <math>''n'' = 13, ''k'' = 3</math>, 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"

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! | 14

|-

! ''K''<mathsub>3</sub>K_3(''n'',1)</math>

| '''1'''

| '''3'''

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| '''59049'''

| 166610-177147

|}

== Applications ==