Hostname: page-component-7479d7b7d-c9gpj Total loading time: 0 Render date: 2024-07-11T04:47:26.387Z Has data issue: false hasContentIssue false
  • English
  • Français

Block Intersections in Balanced Incomplete Block Designs

Published online by Cambridge University Press:  20 November 2018

R. G. Stanton  and
D. A. Sprott
R. G. Stanton
Affiliation:
University of Waterloo
D. A. Sprott
Affiliation:
University of Waterloo
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

One of the most interesting of the smaller BIBD's is the system (8, 14, 7, 4, 3), where we write the parameters in the standard order v, b, r, k, λ. One representation of a design with these parameters is 1248, 3567; 2358, 1467; 3468, 1257; 4578, 1236; 5618,2347; 6728,1345; 7138,2456. This particular design has the feature that every block B is paired with a complementary block B' consisting of all varieties not lying in B. Thus

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 7 , Issue 4 , December 1964 , pp. 539 - 548
Copyright
Copyright © Canadian Mathematical Society 1964

References

1. Bose, R. C., A note on the resolvability of balanced incomplete block designs, Sankhya 6 (1942), 105–110.Google Scholar
2. Fisher, R. A., An examination of different possible solutions in incomplete blocks, Ann. Eugenics 10 (1940), 52–75.CrossRefGoogle Scholar
3. Parker, E. T., Remarks on balanced incomplete block designs, Proc. Amer. Math. Soc. 14 (1963), 729–730.CrossRefGoogle Scholar
4. Seiden, E., A supplement to Parker's "Remarks on balanced incomplete block designs", Proc. Amer. Math. Soc. 14 (1963), 731–732.Google Scholar
5. Stanton, R. G., A Note on BIBDs, Ann. Math. Stat. 28 (1957), 1054–1055.CrossRefGoogle Scholar