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A new infinite class of S (3, {4, 5, 7}, v )
Author(s) -
Ji Lijun,
Zhang Shaopu
Publication year - 2012
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.20303
Subject(s) - combinatorics , mathematics , integer (computer science) , block (permutation group theory) , element (criminal law) , class (philosophy) , order (exchange) , set (abstract data type) , property (philosophy) , discrete mathematics , computer science , law , philosophy , finance , epistemology , artificial intelligence , political science , economics , programming language
A t‐wise balanced design ( a t BD) of order v and block sizes from K , denoted by S ( t , K , v ), is a pair ( X , ℬ ), where X is a v ‐element set and ℬ is a set of subsets of X , called blocks , with the property that | B |∈ K for any B ∈ℬ and every t ‐element subset of X is contained in a unique block. In this article, we shall show that there is an S ( 3 , { 4 , 5 , 7 }, v ) for any positive integer v ≡ 7 ( mod12 ) with v ≠ 19 . Copyright © 2011 Wiley Periodicals, Inc. J Combin Designs 20:68–80, 2012
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