THE THEORETICAL INVESTIGATION OF THE BLOCK DESIGNS.
NIHON UNIV TOKYO DEPT OF STATISTICS
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The report is divided into seven sections. A brief exposition of the incidence matrix of the balanced incomplete block BIB design is given in section 1. The Hasse-Minkowski p-invariant of the rational congruence is discussed in section 2. In section 3, the necessary condition for existence of a symmetrical BIB design is given in terms of the Hasse-Minkowski p-invariant as the prototype of the non-existence proofs. In section 4, the properties of the association algebra of an association are presented with some examples of association schemes. Section 5 is devoted to the derivation of the necessary condition for existence of a regular and symmetrical partially balanced incomplete block PBIB design. The argument presented in section 5 is immediately carried over in section 6 to the derivation of the necessary condition for existence of a certain class of asymmetric PBIB designs. In section 7, the relationship algebra of a PBIB design is explained and some discussions of the non-existence proofs in connection with the relationship algebra are presented. Author
- Statistics and Probability