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Decomposable super‐simple NRBIBDs with block size 4 and index 6
Author(s) -
Yu Huangsheng,
Sun Xianwei,
Wu Dianhua,
Abel R. Julian R.
Publication year - 2019
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.21637
Subject(s) - mathematics , simple (philosophy) , pairwise comparison , combinatorics , block (permutation group theory) , block size , block design , component (thermodynamics) , index (typography) , discrete mathematics , statistics , computer science , philosophy , physics , computer security , epistemology , key (lock) , world wide web , thermodynamics
Necessary conditions for the existence of a super‐simple, decomposable, near‐resolvable ( v , 4 , 6 ) ‐balanced incomplete block design (BIBD) whose 2‐component subdesigns are both near‐resolvable ( v , 4 , 3 ) ‐BIBDs are v ≡ 1 (mod 4 ) and v ≥ 17 . In this paper, we show that these necessary conditions are sufficient. Using these designs, we also establish that the necessary conditions for the existence of a super‐simple near‐resolvable ( v , 4 , 3 ) ‐RBIBD, namely v ≡ 1 (mod 4 ) and v ≥ 9 , are sufficient. A few new pairwise balanced designs are also given.