New upper bounds for the football pool problem for 6, 7, and 8 matches
نویسندگان
چکیده
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منابع مشابه
The Inverse Football Pool Problem
The minimal number of spheres (without “interior”) of radius n required to cover the finite set {0, . . . , q−1} equipped with the Hamming distance is denoted by T (n, q). The only hitherto known values of T (n, q) are T (n, 3) for n = 1, . . . , 6. These were all given in the 1950s in the Finnish football pool magazine Veikkaaja along with upper and lower bounds for T (n, 3) for n ≥ 7. Recentl...
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We derive several new lower bounds on the size of ternary covering codes of lengths 6, 7 and 8 and with covering radii 2 or 3.
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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 k...
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ورودعنوان ژورنال:
- J. Comb. Theory, Ser. A
دوره 52 شماره
صفحات -
تاریخ انتشار 1989