Construction of Some Resolvable t-designs
Science Journal of Applied Mathematics and Statistics
Volume 5, Issue 1, February 2017, Pages: 49-53
Received: Jul. 20, 2016; Accepted: Aug. 8, 2016; Published: Feb. 22, 2017
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Author
Alilah David, Department of Mathematics, Masinde Muliro University of Science and Technology, Nairobi, Kenya
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Abstract
The 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. In this study t-design is constructed by relating known BIB designs, combinatorial designs and algebraic structures with t-designs. Additionally, an alternative approach for the construction of t-designs that provides a unified framework is also presented.
Keywords
Block Designs, Resolvable Designs, t-designs
To cite this article
Alilah David, Construction of Some Resolvable t-designs, Science Journal of Applied Mathematics and Statistics. Vol. 5, No. 1, 2017, pp. 49-53. doi: 10.11648/j.sjams.20170501.17
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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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