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Bhartiya Krishi Anusandhan Patrika, volume 37 issue 1 (march 2022) : 8-12

Partially Balanced 3-Designs using Mutually Orthogonal Latin Squares

Sayantani Karmakar, Cini Varghese, Seema Jaggi, Mohd Harun, Devendra Kumar
1ICAR-Indian Agricultural Statistics Research Institute, Pusa-110 012, New Delhi, India.

  • Submitted09-08-2021|

  • Accepted12-03-2022|

  • First Online 12-04-2022|

  • doi 10.18805/BKAP351

Cite article:- Karmakar Sayantani, Varghese Cini, Jaggi Seema, Harun Mohd, Kumar Devendra (2022). Partially Balanced 3-Designs using Mutually Orthogonal Latin Squares. Bhartiya Krishi Anusandhan Patrika. 37(1): 8-12. doi: 10.18805/BKAP351.

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.

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