Construction Procedure for Non-trivial T-designs
American Journal of Theoretical and Applied Statistics
Volume 6, Issue 1, January 2017, Pages: 52-60
Received: Jul. 20, 2016; Accepted: Aug. 8, 2016; Published: Feb. 22, 2017
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Authors
John Chibayi, Department of Statistics and Actuarial Science, MasenoUniverisity, Nairobi, Kenya
David Alila, Department of Mathematics, MasindeMuliro University of Science and Technology, Nairobi, Kenya
Fredrick Onyango, Department of Statistics and Actuarial Science, MasenoUniverisity, Nairobi, Kenya
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Abstract
A t-design is a generation of balanced incomplete block design (BIBD) where λ is not restricted to the blocks in which a pair of treatments occurs but to the number of blocks in which any t treatments (t = 2,3…) occurs. The problem of finding all parameters (t, v, k, λt) for which t-(v, k, λt) design exists is a long standing unsolved problem especially with λ=1 (Steiner System) as no Steiner t-designs are known for t ≥ 6 when v > k. The objective of this study therefore to develop new methods of constructing t-designs with t ≥ 3 and λ ≥1. In this study t-design is constructed by relating known BIB designs, combinatorial designs and algebraic structures with t-designs.
Keywords
Block Designs, Steiner Systems, T-designs
To cite this article
John Chibayi, David Alila, Fredrick Onyango, Construction Procedure for Non-trivial T-designs, American Journal of Theoretical and Applied Statistics. Vol. 6, No. 1, 2017, pp. 52-60. doi: 10.11648/j.ajtas.20170601.17
Copyright
Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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