Publikation: Construction, Application and Extension of Resolvable Balanced Incomplete Block Designs in the Design of Experiments
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2017
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Bachelorarbeit
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Zusammenfassung
This overview provides the foundation to explore the practicality of RBIBD and optimal KP in the design of experiments in order to create designs with fixed block size k and v points, k|v. We clarify the mathematical restrictions and possibilities of those designs. For this, we collect methods to construct RBIBD and KP. We see that for k=2 all RBIBD can be constructed with ease and for k=3 quite some methods do construct a lot of them. An overview shows the results of this thesis regarding k=3. We transform some of the methods to algorithms, also we clarify the upper bound for arbitrary k, giving a proof and present the results for various k. Further, we transform the theorem of doubling construction and introduce a method and show the difficulties and possibilities for improvement in this method. We introduce an extension to this method to construct a family of non-optimal Kirkman packing designs with r = M(v)-1.
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Resolvable Balanced Incomplete Block Designs, Steiner Triple Systems, Kirkman Packing Designs, Nearly Kirkman Triple System
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FISSLER, Steffen, 2017. Construction, Application and Extension of Resolvable Balanced Incomplete Block Designs in the Design of Experiments [Bachelor thesis]. Konstanz: Universität KonstanzBibTex
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Prüfungsdatum der Dissertation
Hochschulschriftenvermerk
Konstanz, Universität Konstanz, Bachelorarbeit, 2017
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