ISSN: 2226-6348
Open access
Some new series of three associate Partially Balanced Incomplete Block Designs with minimal blocks and two replicates have been constructed by introducing another blank diagonal entry to triangular association scheme. The generalization of parameters for any even positive integer n greater than or equal to eight have also been given. Specific design has also been constructed to illustrate the results numerically.
Agrawal, H., & Prasad, J. (1984), “Construction of partially balanced incomplete block designs with nested rows and columns.” Biom. J 26, 883–891
Arya, A. S., & Prem, N. (1981), “Truncated triangular association scheme and related partial diallel crosses” Sankhya: Indian journal of statistics 43 B, Pt 1, 93-103.
Atiqulla, M. (1958), “On configuration and non-isomophisim of some incomplete block designs” Indian journal of statistics, 20 series 3, 4, 227-248
Bose, R. C., Nair, K. R. (1939), “Partially Balanced Incomplete Block designs” Sankhya 4, 337-372
Cheng, C-S., Constance, G. M., Hedayat, A. S. (1984), “A unified method for constructing PBIB designs based on triangular and L2-schemes” J.R.statist.soc 46, 1, 31-37.
Garg, D. K., Jhaji, H. S., & Mishra, G. (2011), “Construction of Some New Triangular and Four Associate Class PBIB Designs with Two Replicates” International Journal of Mathematical Sciences and Applications 1, 2, 808-821.
Kishore, S., Sanpei, K. (2004), “Some series of block designs with nested rows and columns.” Australasian journal of combinatorics. 29, 337–347.
John, P. W. M. (1966), “An extension of the triangular association scheme to three associate classes.” J. Roy. Statist. Soc B, 28, 361–365.
Shrikhande, S. S. (1960), “Relations between certain incomplete block designs”, In: Contributions to Probability and Statistics. I. Olkin (ed.). Stanford, CA: Stanford University Press, 388–395.
Shrikhande, S. S. (1965), “On a class of partially balanced incomplete block designs”, Ann. Math. Statist 36, 1807–1814.
In-Text Citation: (Rambaei et al., 2012)
To Cite this Article: Rambaei, S. J. K., Kipkemoi, C. E., & Kipkosgei, T. I. (2012). Construction of Some New Three Associate Class PBIB Designs with Two Replicates. International Journal of Academic Research in Progressive Education and Development, 1(2), 133–138.
Copyright: © 2021 The Author(s)
Published by HRMARS (www.hrmars.com)
This article is published under the Creative Commons Attribution (CC BY 4.0) license. Anyone may reproduce, distribute, translate and create derivative works of this article (for both commercial and non-commercial purposes), subject to full attribution to the original publication and authors. The full terms of this license may be seen at: http://creativecommons.org/licences/by/4.0/legalcode