Covering code: Difference between revisions

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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 predictreplicate thea resultsbet ofon ''n'' football matches asto be a home win, draw or away win with at most ''R'' 'misses', orby toplacing atmultiple leastbets predictthat all {{nowrap|''n'' -matches 1}}will ofend thema withcertain multiple betsway. Thus, for ''n'' matches with at most one 'miss', a ternary covering, ''K''₃(''n'',1), is sought.

If <math>n=\tfrac12 (3^k-1)</math> then 3^''n''-''k'' 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