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Some Configurations in Finite Projective Spaces and Partially Balanced Incomplete Block Designs

Published online by Cambridge University Press:  20 November 2018

D. K. Ray-Chaudhuri
D. K. Ray-Chaudhuri*
Affiliation:
I.B.M., Yorktown Heights, N.Y.
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Using the methods developed in (2 and 3), in this paper we study some properties of the configuration of generators and points of a cone in an w-dimensional finite projective space. The configuration of secants and external points of a quadric in a finite plane of even characteristic is also studied. I t is shown that these configurations lead to several series of partially balanced incomplete block (PBIB) designs. PBIB designs are defined in Bose and Shimamoto (1). A PBIB design with m associate classes is an arrangement of v treatments in b blocks such that.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 17 , 1965 , pp. 114 - 123
Copyright
Copyright © Canadian Mathematical Society 1965

References

1. Bose, R. C. and Shimamoto, T., Classification and analysis of partially balanced incomplete block designs with two associate classes, J. Amer. Statist. Ass., 47 (1952), 151–184.Google Scholar
2. Ray-Chaudhuri, D. K., Some results on quadrics infinite projective geometry based on galois fields, Can. J. Math., 14 (1962), 129–138.Google Scholar
3. Ray, D. K.-Chaudhuri, Application of the geometry of quadrics for constructing PBIB designs, Ann. Math. Statistics, 33 (1962), 1175–1186.Google Scholar