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It is known that group divisible designs (GDDs) with [email protected]"1+1 are regular and symmetric, and that the combinatorial structure of these designs is characterized in terms of Hadamard tournaments and strongly regular graphs. In this paper, it is shown that GDDs without @a-resolution classes in each group are also specified by Hadamard tournaments and strongly regular graphs. The result given by Jimbo and Kageyama (ICA Bull. 32 (2001) 29) is included in the present result as a special case.

Balanced nested designs are closely related to other combinatorial structures such as balanced arrays and balanced n-ary designs. In particular, the existence of symmetric balanced nested designs is equivalent to the existence of some balanced arrays. In this paper, various constructions for symmetric balanced nested designs are provided. They are used to determine the spectrum of symmetric balanced nested balanced incomplete block designs with block size 3 and 4.

This provides a comprehensive listing of books, mainly in English, on the topic of experimental design relative to historical development, classification, construction, experimental layout, and statistical analysis. The books can be used as texts in courses and as references for research. It should be noted that most of the material presented in books places the emphasis on statistical analysis with little or nothing said about statistical design of an experiment. Construction and combinatorics of experimental design are entrenched as a branch of finite mathematics. Books in such areas are also listed. Published books presented at conferences on experimental design are also scanned. In addition, this list includes books and papers on experimental design presented in statistical conferences. Available textbooks with chapter(s) on experi- mental design are also mentioned. We have been selective, however, with conference- books and books in applications of design. An earlier version (1981) of our bibliogra- phy of books on experimental design listed 235 titles. The number of such books continues to grow, and the second version (1982) contained 396 titles. The present listing contains 625 titles. 2.

During the last three decades, the robustness of experimental designs has been investigated under several criteria. The present paper surveys various results on robustness of block designs in three different directions, when some observations are missing. The criteria on robustness discussed here are taken up from a combinatorial point of view.

The family of block designs is of importance in statistical design theory because of its appealing combinatorial and statistical properties. Block designs have opened up many interesting and challenging problems in combinatorial mathematics. This survey focuses on block designs with the properties of connectedness, classification and balancing, resolvability, and inequality and characterization from a combinatorial point of view.

In this paper, some μ-resolvable balanced incomplete block designs are constructed. Furthermore, parameters' combinations of all the designs constructed are tabulated under some restrictions.

It is known that there are some lower bounds for the number of blocks in a balanced incomplete block design (BIBD). Especially, Fisher's inequality b ⩾ v is well-known for a BIBD with parameters v, b, r, k and λ. Fisher's inequality can be improved upon if one puts additional restrictions on a BIBD. Artificial restrictions are infinite in number so is the number of new bounds. The condition of non-symmetry on the design discussed here is a very simple restriction. The main purpose of this paper is to give improvements of inequalities for BIBDs with the only condition of non-symmetry. Improved inequalities appear to be the best for any non-symmetrical BIBD.

Methods of construction of group divisible partially balanced bipartite block designs are presented. These designs have unequal replications of treatments.