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Partially Balanced 3-Designs using Mutually Orthogonal Latin Squares

DOI: 10.18805/BKAP351    | Article Id: BKAP351 | Page : 8-12
Citation :- Partially Balanced 3-Designs using Mutually Orthogonal Latin Squares.Bhartiya Krishi Anusandhan Patrika.2022.(37): 8-12
Sayantani Karmakar, Cini Varghese, Seema Jaggi, Mohd Harun, Devendra Kumar mohd.harun@icar.gov.in
Address : ICAR-Indian Agricultural Statistics Research Institute, Pusa-110 012, New Delhi, India.
Submitted Date : 9-08-2021
Accepted Date : 12-03-2022

Abstract

t-designs represent a generalized class of balanced incomplete block designs in which the number of blocks in which any t treatments (t ≥ 2) occur together is a constant. Like other families of incomplete block designs, t-designs find potential application in farming system research where the main concern would be to select the best combination out of a certain set of t-component farming systems for a specific agro-ecological zone. But in order to obtain t-balance we may require large number of blocks and replications. Partially balanced t-designs are introduced for experimental situations where it is not possible to get t-balanced designs. A series of partially balanced 3-designs are constructed using mutually orthogonal Latin Squares. These designs, though possess pair-wise balance, are not combinatorially balanced in terms of 3-tuples. They also satisfy the properties of 3-packing designs. The efficiency factor of these designs is quite high as v increases, the efficiency increases.

Keywords

Balanced incomplete block designs Canonical efficiency factor Mutually orthogonal latin squares t-packing

References

  1. Assaf, A.M. and Shalaby, N. (1992). Packing design with block size 5 and indices 8, 12, 15.  Journal of Combinatorial Theory. 59: 23-30.
  2. David, A. (2017). Construction of some resolvable t- designs. Science Journal of Applied Mathematics and Statistics. 5(1): 49-53.
  3. Hartman, A. (1986). On small packing and covering designs with block size 4. Discrete Mathematics. 59: 275-281.
  4. Hedayat, A. and Kageyama, S. (1980). The Family of t-designs-Part I. Journal of Statistical Planning and Inference. 4: 173-212.
  5. Jha, A., Varghese, C., Jaggi, S., Harun, M. and Kumar, D. (2018a). A new series of resolvable PBIB (2) designs in unequal block sizes with three replicates, Bhartiya Krishi Anusandhan Patrika. 33(1): 161-164.
  6. Jha, A., Varghese, C., Jaggi, S., Harun, M., Kumar, D. (2018b). Resolvable block designs balanced for non-directional neighbour effects. Bhartiya Krishi Anusandhan Patrika. 33(2): 113-115.
  7. Kageyama, S. and Hedayat, A. (1983). The Family of t-designs-Part II. Journal of Statistical Planning and Inference. 7: 257-287.
  8. Trung, T.V. (2001). Recursive constructions for 3-designs and resolvable 3-designs. Journal of Statistical Planning and Inference. 95: 341-358.
  9. Trung, T.V. (2017). Simple t-designs: A recursive construction for arbitrary t. Designs, Codes and Cryptography. 83(3): 493-502.
  10. Trung, T.V. (2018). A recursive construction for simple t-designs using resolutions. Designs, Codes and Cryptography. 86(6): 1185-1200.
  11. Trung, T.V. (2019). Recursive constructions for s- resolvable t-designs. Design, Codes and Cryptography. 87: 2835-2845.
  12. Varghese, C., Jaggi, S., Harun, M., Kumar, D. (2020). Three-associate class partially balanced incomplete block designs through kronecker product. Bhartiya Krishi Anusandhan Patrika.  35(1 and 2): 102-105.

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