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Upper bounds on the general covering number C λ ( v , k , t , m )
Author(s) -
Bertolo Riccardo,
Bluskov Iliya,
Hämäläinen Heikki
Publication year - 2004
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.20019
Subject(s) - combinatorics , mathematics , upper and lower bounds , block (permutation group theory) , lambda , physics , mathematical analysis , optics
Abstract A collection $\cal C$ of k ‐subsets (called blocks ) of a v ‐set X ( v ) = {1, 2,…, v } (with elements called points ) is called a t ‐( v , k , m , λ) covering if for every m ‐subset M of X ( v ) there is a subcollection $\cal K$ of $\cal C$ with $|\cal K|\geq \lambda$ such that every block K ∈ $\cal K$ has at least t points in common with M . It is required that v ≥ k ≥ t and v ≥ m ≥ t . The minimum number of blocks in a t ‐( v , k , m , λ) covering is denoted by C λ ( v , k , t , m ). We present some constructions producing the best known upper bounds on C λ ( v , k , t , m ) for k = 6, a parameter of interest to lottery players. © 2004 Wiley Periodicals, Inc.