Lower Bounds for the Football Pool Problem for 7 and 8 Matches

Let k3(n) denote the minimal cardinality of a ternary code of length n and covering radius one. In this paper we show k3(7) ≥ 156 and k3(8) ≥ 402 improving on the best previously known bounds k3(7) ≥ 153 and k3(8) ≥ 398. The proofs are founded on a recent technique of the author for dealing with systems of linear inequalities satisfied by the number of elements of a covering code, that lie in kdimensional subspaces of Fn 3 .

• Type: Journal
• Year: 2007
• Where: COMBINATORICS
• Authors: Wolfgang Haas
• Keywords: COMBINATORICS 2007, Linear Inequalities, Minimal Cardinality, Ternary Code