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A new infinite class of S(3, {4, 5, 7}, v)
Article first published online: 22 NOV 2011
DOI: 10.1002/jcd.20303
Copyright © 2011 Wiley Periodicals, Inc.
Additional Information
How to Cite
Ji, L. and Zhang, S. (2012), A new infinite class of S(3, {4, 5, 7}, v). J. Combin. Designs, 20: 68–80. doi: 10.1002/jcd.20303
Publication History
- Issue published online: 28 NOV 2011
- Article first published online: 22 NOV 2011
- Manuscript Revised: 23 JUL 2011
- Manuscript Received: 26 JAN 2011
Funded by
- NSFC. Grant Numbers: 10701060, 10831002
- Qing Lan Project of Jiangsu Province (to L. Ji); NSFC. Grant Number: 11001182 (to S. Zhang)
- Abstract
- Article
- References
- Cited By
Keywords:
- t-wise balanced design;
- s-fan design;
- candelabra t-system
Abstract
A t-wise balanced design (atBD) 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