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New upper bounds on the minimum size of covering designs
Author(s) -
Bluskov Iliya,
Hämäläinen Heikki
Publication year - 1998
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/(sici)1520-6610(1998)6:1<21::aid-jcd2>3.0.co;2-y
Subject(s) - combinatorics , mathematics , block size , block (permutation group theory) , upper and lower bounds , cover (algebra) , set (abstract data type) , discrete mathematics , computer science , mechanical engineering , mathematical analysis , computer security , key (lock) , engineering , programming language
Let D = { B 1 , B 2 ,…, B b } be a finite family of k ‐subsets (called blocks ) of a v ‐set X ( v ) = {1, 2,…, v } (with elements called points ). Then D is a ( v , k , t ) covering design or covering if every t ‐subset of X ( v ) is contained in at least one block of D . The number of blocks, b , is the size of the covering, and the minimum size of the covering is called the covering number , denoted C ( v , k , t ). This article is concerned with new constructions of coverings. The constructions improve many upper bounds on the covering number C ( v , k , t ) © 1998 John Wiley & Sons, Inc. J Combin Designs 6:21–41, 1998