Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-26T12:00:34.970Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Block Structure of Quartic Designs

Published online by Cambridge University Press:  20 November 2018

C. D. O'Shaughnessy
C. D. O'Shaughnessy*
Affiliation:
University of Saskatchewan, Saskatoon, Saskatchewan
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.

Raghavarao and Chandrasekhararao [3] introduced a family of PBIB designs having three associate classes known as cubic designs. In this paper a detailed analysis of the case of PBIB designs having four associate classes, which are called quartic designs, is given. Results are obtained pertaining to construction and existence of quartic designs. Moreover, using methods similar to those used by Shah [5], [6], [7], the block structure of certain quartic designs is studied.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 14 , Issue 3 , September 1971 , pp. 377 - 389
Copyright
Copyright © Canadian Mathematical Society 1971

References

1. Connor, W. S. and Clatworthy, W. H., Some theorems for partially balanced designs, Ann. Math. Statist. 25 (1954), 100-112.Google Scholar
2. Ogawa, Junjiro, A necessary condition for the existence of regular and symmetrical experimental designs of triangular type, with partially balanced incomplete blocks, Ann. Math. Statist. 30 (1959), 1063-1071.Google Scholar
3. Raghavarao, D. and Chandrasekhararao, K., Cubic designs, Ann. Math. Statist. 35 (1964), 389-397.Google Scholar
4. Shah, B. V., A generalization of partially balanced incomplete block designs, Ann. Math. Statist. 30 (1959), 1041-1050.Google Scholar
5. Shah, S. M., An upper bound for the number of disjoint blocks in certain PBIB designs, Ann. Math. Statist. 35 (1964), 398-407.Google Scholar
6.Shah, S. M., Bounds for the number of common treatments between any two blocks of certain PBIB designs, Ann. Math. Statist. 36 (1965), 337-342.Google Scholar
7. Shah, S. M., On the block structure of certain partially balanced incomplete block designs, Ann. Math. Statist. 37 (1966), 1016-1020.Google Scholar
8. Shrikhande, S. S. and Jain, N. C., The non-existence of some partially balanced incomplete block designs with Latin square type association scheme, Sankhyā Ser. A, 24 (1966), 259-268.Google Scholar
9. Shrikhande, S. S., Raghavarao, D., and Tharthare, S. K., Non-existence of some unsymmetrical partially balanced incomplete block designs, Canad. J. Math. 15 (1963), 686-701.Google Scholar