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New upper bounds for the football pool problem for 11 and 12 matches. (English)
J. Comb. Theory, Ser. A 67, No.2, 161-168 (1994).
Author’s summary: We consider the problem of minimizing the number of words in a code with the property that all words in the space $F\sp n\sb 3$ are within Hamming distance 1 from some codeword. This problem is called the football pool problem, since the words in such a code can be used in a football pool to guarantee that at least one forecast has at least $n - 1$ correct results. In this note we show that for 11 and 12 matches, there are 9477 and 27702 words, respectively, having the aforementioned property. Simulated annealing [cf. {\it L. T. Wille}, J. Comb. Theory, Ser. A 45, 171-177 (1987; Zbl 0667.05018)] has played an important role in the search for these words.
R.-H.Schulz (Berlin)