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Design theory. (English) Zbl 0569.05002
Mannheim-Wien-Zürich: Bibliographisches Institut, B.I.- Wissenschaftsverlag. 688 p. DM 128.00 (1985).
Contents: I. Examples and basic definitions. II. Combinatorial analysis of designs. III. Groups and Designs. IV. Witt designs and Mathieu groups. V. Highly transitive groups. VI. Difference sets and regular symmetric designs. VII. Difference families. VIII. Further direct constructions. IX. Recursive constructions. X. Transversal designs and nets, continued. XI. Asymptotic existence theory. XII. Characterizations of classical designs.
In addition to the above contents there is a 33 page appendix of tables giving the construction and existence remarks for several classes of designs discussed in the text.
This book is an excellent up-to-date treatise on balanced incomplete block designs, t-designs, pairwise balanced designs, orthogonal latin squares and orthogonal arrays with respect to their combinatorial problems, constructions and existence. It will be a highly useful reference book for researchers working on incidence structures of block designs. This book is essentially intended for and aimed at combinatorial mathematicians.
Reviewer: D.Raghavarao

MSC:
05-02 Research exposition (monographs, survey articles) pertaining to combinatorics
05B05 Combinatorial aspects of block designs
62K10 Statistical block designs
05B10 Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.)
05B15 Orthogonal arrays, Latin squares, Room squares
05B30 Other designs, configurations