Accession Number:

AD0678209

Title:

THE THEORETICAL INVESTIGATION OF THE BLOCK DESIGNS.

Descriptive Note:

Final rept.,

Corporate Author:

NIHON UNIV TOKYO DEPT OF STATISTICS

Personal Author(s):

Report Date:

1968-06-01

Pagination or Media Count:

46.0

Abstract:

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

Subject Categories:

  • Statistics and Probability

Distribution Statement:

APPROVED FOR PUBLIC RELEASE