Main Article Content
Abstract
Many popular neighbor designs are used in serology, agriculture, and forestry which manifest neighbor effects very much. If every treatment appears as a neighbor with other (v-2) treatments once but emerges twice with only one treatment, such designs are called Quasi Rees neighbor designs (QRNDs) in k size of circular blocks. These designs were used for counterbalancing the neighboring effects for the cases for which minimal neighbor designs cannot be constructed. In this article, various generators are constructed to obtain circular binary NDs, using cyclic shifts.
Keywords
Article Details

This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following License
CC BY: This license allows reusers to distribute, remix, adapt, and build upon the material in any medium or format, so long as attribution is given to the creator. The license allows for commercial use.
References
- Ahmed, R., Akhtar, M. (2008). Construction of neighbor balanced block designs. Journal of Statistical Theory and Practice, 2 (4), 551- 558.
- Ahmed, R., Akhtar, M. and Tahir, M. H. (2009). Economical generalized neighbor designs of use in Serology. Computational Statistics and Data Analysis, 53, 4584-4589.
- Ahmed, R. and Akhtar, M. (2011). Designs balanced for neighbor effects in circular blocks of size six. Journal of Statistical Planning and Inference, 141, 687-691.
- Ahmed, R., Akhtar, M. and Yasmin, F. (2011). Brief review of one dimensional neighbor balanced designs since 1967. Pakistan Journal of Commerce and Social Sciences, 5(1), 100-116.
- Akhtar, M., Ahmed, R. and Yasmin, F. (2010). A catalogue of nearest neighbor balanced designs in circular blocks of size five. Pakistan Journal of Statistics, 26(2), 397- 405.
- Azais, J. M., Bailey, R. A. and Monod, H. (1993). A catalogue of efficient neighbour- designs with border plots. Biometrics, 49 (4), 1252- 61.
- Cheng, C.S. (1983). Construction of optimal balanced incomplete block designs for correlated observations. Annals of Statistics, 11, 240-246.
- Hwang, F. K. (1973). Constructions for some classes of neighbor designs. Annals of Statistics, 1(4) 786- 790.
- Iqbal, I. (1991). Construction of experimental design using cyclic shifts. Unpublished Ph.d Thesis. U.K: University of Kent at Canterbury.
- Iqbal, I., Tahir, M.H. and Ghazali, S.S.A. (2009). Circular neighbor-balanced designs using cyclic shifts. Science in China, Series A: Mathematics, 52(10), 2243- 2256.
- Lawless, J. F. (1971). A note on certain types of BIBDs balanced for residual effects. Annals of Mathematics and Statistics, 42, 1439-1441.
- Preece, D. A. (1994). Balanced Ouchterlony neighbor designs. Journal of Combinatorial Mathematics and Combinatorial Computing, 15, 197–219.
- Rees, D. H. (1967). Some designs of use in serology. Biometrics, 23, 779- 791.
- Shahid, M. R., Zakria, M., Shehzad, F. and Ahmed, R. (2017). Some important classes of generalized neighbor designs in linear blocks. Communications in Statistics-Simulation and Computation. 46(3), 1991-1997.
- ZafarYab, M., Shehzad, F. and Ahmed, R. (2010). Proper generalized neighbor designs in circular blocks. Journal of Statistical Planning and Inference, 140(11), 3498-3504.