A new lower bound for the football pool problem for 7 matches
Journal de théorie des nombres de Bordeaux, Tome 8 (1996) no. 2, pp. 481-484.

Notons K 3 (7,1) le cardinal minimal d’un code ternaire de longueur 7 et de rayon de recouvrement un. Dans un précédent article, nous avons amélioré la minoration K 3 (7,1)147 en montrant que K 3 (7,1)150. Dans cette note, nous prouvons que K 3 (7,1)153.

Let K 3 (7,1) denote the minimum cardinality of a ternary code of length 7 and covering radius one. In a previous paper, we improved on the lower bound K 3 (7,1)147 by showing that K 3 (7,1)150. In this note, we prove that K 3 (7,1)153.

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     author = {Laurent Habsieger},
     title = {A new lower bound for the football pool problem for $7$ matches},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {481--484},
     publisher = {Universit\'e Bordeaux I},
     volume = {8},
     number = {2},
     year = {1996},
     zbl = {0866.94027},
     mrnumber = {1438484},
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     url = {https://jtnb.centre-mersenne.org/item/JTNB_1996__8_2_481_0/}
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Laurent Habsieger. A new lower bound for the football pool problem for $7$ matches. Journal de théorie des nombres de Bordeaux, Tome 8 (1996) no. 2, pp. 481-484. https://jtnb.centre-mersenne.org/item/JTNB_1996__8_2_481_0/

[1] W. Chen And I.S. Honkala, Lower bounds for q-ary covering codes, IEEE Trans. Inform. Theory 36 (1990), 664-671. | MR | Zbl

[2] G.D. Cohen, S.N. Litsyn, A.C. Lobstein and H.F. Mattson, Covering radius 1985-1994, preprint.

[3] L. Habsieger, Lower bounds for q-ary coverings by spheres of radius one, J. Combin. Theory Ser. A 67 (1994), 199-222. | MR | Zbl

[4] L. Habsieger, Binary codes with covering radius one: some new lower bounds, Discrete Mathematics, to appear. | MR | Zbl