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Two new infinite families of extremal class‐uniformly resolvable designs
Author(s) -
Dinitz J.H.,
Ling Alan C.H.
Publication year - 2008
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.20165
Subject(s) - mathematics , combinatorics , class (philosophy) , resolution (logic) , discrete mathematics , artificial intelligence , computer science
In 1991, Lamken et al. [7] introduced the notion of class‐uniformly resolvable designs, CURDs. These are resolvable pairwise balanced designs PBD( v , K , λ) in which given any two resolution classes C and C ', for each k ∈ K the number of blocks of size k in C is equal to the number of blocks of size k in C '. Danzinger and Stevens showed that if a CURD has v points, then v ≤ (3 p 3 ) 2 and v ≤ ( p 2 ) 2 where p i denotes the number of blocks of size i for i = 2, 3. They then constructed an infinite class of extremal CURDs with v = (3 p 3 ) 2 when p 3 is odd and an infinite class with v = ( p 2 ) 2 when p 2 ≡ 2 (mod 6). In this note, we construct two new infinite families of extremal CURDs, when v = (3 p 3 ) 2 for all p 3 ≥ 1 and when v = ( p 2 ) 2 with p 2 ≡ 0 (mod 3) except possibly when p 2 = 12. © 2007 Wiley Periodicals, Inc. J Combin Designs 16: 213–220, 2008