Construction, Application and Extension of Resolvable Balanced Incomplete Block Designs in the Design of Experiments

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.publishe