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

Let ${K}_{3}\left(7,1\right)$ 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 ${K}_{3}\left(7,1\right)\ge 147$ by showing that ${K}_{3}\left(7,1\right)\ge 150$. In this note, we prove that ${K}_{3}\left(7,1\right)\ge 153$.

Notons ${K}_{3}\left(7,1\right)$ 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 ${K}_{3}\left(7,1\right)\ge 147$ en montrant que ${K}_{3}\left(7,1\right)\ge 150$. Dans cette note, nous prouvons que ${K}_{3}\left(7,1\right)\ge 153$.

@article{JTNB_1996__8_2_481_0,
author = {Habsieger, Laurent},
title = {A new lower bound for the football pool problem for $7$ matches},
journal = {Journal de th\'eorie des nombres de Bordeaux},
publisher = {Universit\'e Bordeaux I},
volume = {8},
number = {2},
year = {1996},
pages = {481-484},
zbl = {0866.94027},
mrnumber = {1438484},
language = {en},
url = {http://www.numdam.org/item/JTNB_1996__8_2_481_0}
}

Habsieger, Laurent. A new lower bound for the football pool problem for $7$ matches. Journal de théorie des nombres de Bordeaux, Volume 8 (1996) no. 2, pp. 481-484. http://www.numdam.org/item/JTNB_1996__8_2_481_0/

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