Abstract
The family of t-designs is one the most important family of statistical designs. These designs can be used to construct other significant designs. In this paper, an attempt has been made to construct Third Order Rotatable Designs (TORDs) in both symmetric and asymmetric levels using t-designs of unequal set sizes, i.e. UE-t designs. In most cases, the obtained design has lesser run size than third-order designs already in existence. A list of proposed classes of designs has been presented along with their G-efficiency.
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Acknowledgements
We are thankful to the Editor-in-Chief and the reviewers for the critical evaluation of the earlier draft that have led to a considerable improvement in the structure of the manuscript. We acknowledge the facilities provided by ICAR-IASRI, New Delhi, P.G. School, IARI, New Delhi, ICAR-CMFRI, Kochi for conducting the research. Financial assistance received from the Indian Council of Agricultural Research, Govt. of India is also duly acknowledged.
Funding
Indian Council of Agricultural Research (ICAR)-Junior Research Fellowship (Ankita Verma); ICAR-LBS Young Scientist Award project (Eldho Varghese).
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Appendix
Appendix
t-designs of unequal set sizes, UE-t design for 4 \(\le\) v \(\le\) 9.
(4, 8, 5, 4 \(\times\) 2, 4 \(\times\) 3, 3, 1) | (5, 20, 10, 10 \(\times\) 3, 10 \(\times\) 2, 4, 1) | (6, 14, 7, 3 \(\times\) 2, 8 \(\times\) 3, 3 \(\times\) 4, 3, 1) | |||||||
|---|---|---|---|---|---|---|---|---|---|
3 | 4 | 1 | 2 | 6 | 2 | ||||
1 | 3 | 1 | 3 | 1 | 3 | ||||
1 | 2 | 1 | 4 | 4 | 5 | ||||
2 | 4 | 1 | 5 | 1 | 2 | 4 | |||
1 | 2 | 3 | 2 | 3 | 2 | 3 | 4 | ||
1 | 2 | 4 | 2 | 4 | 3 | 4 | 6 | ||
1 | 3 | 4 | 2 | 5 | 5 | 6 | 1 | ||
2 | 3 | 4 | 3 | 4 | 3 | 5 | 6 | ||
3 | 5 | 1 | 4 | 6 | |||||
4 | 5 | 1 | 2 | 5 | |||||
1 | 2 | 3 | 2 | 3 | 4 | ||||
1 | 2 | 4 | 1 | 2 | 3 | 6 | |||
1 | 2 | 5 | 1 | 3 | 4 | 5 | |||
1 | 3 | 4 | 2 | 4 | 5 | 6 | |||
1 | 3 | 5 | |||||||
1 | 4 | 5 | |||||||
2 | 3 | 4 | |||||||
2 | 3 | 5 | |||||||
2 | 4 | 5 | |||||||
3 | 4 | 5 | |||||||
(7, 14, 7, 7 \(\times\) 3, 7 \(\times\) 4, 3, 1) | (8, 16, 8, 8 \(\times\) 5, 8 \(\times\) 3, 4, 2) | (9, 24, 12, 12 \(\times\) 3, 12 \(\times\) 6, 6, 3) | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 2 | 4 | 2 | 4 | 8 | |||||||||
2 | 3 | 5 | 1 | 2 | 5 | 1 | 2 | 3 | ||||||
3 | 4 | 6 | 1 | 3 | 8 | 4 | 5 | 6 | ||||||
4 | 5 | 7 | 2 | 6 | 7 | 7 | 8 | 9 | ||||||
5 | 6 | 1 | 3 | 4 | 6 | 1 | 4 | 7 | ||||||
6 | 7 | 2 | 1 | 4 | 7 | 2 | 5 | 8 | ||||||
7 | 1 | 3 | 3 | 5 | 7 | 3 | 6 | 9 | ||||||
3 | 5 | 6 | 7 | 5 | 6 | 8 | 1 | 5 | 9 | |||||
1 | 4 | 6 | 7 | 1 | 3 | 5 | 6 | 7 | 2 | 6 | 7 | |||
1 | 2 | 5 | 7 | 3 | 4 | 6 | 7 | 8 | 3 | 4 | 8 | |||
1 | 2 | 3 | 6 | 2 | 4 | 5 | 6 | 7 | 1 | 6 | 8 | |||
2 | 3 | 4 | 7 | 1 | 3 | 4 | 5 | 8 | 2 | 4 | 9 | |||
1 | 3 | 4 | 5 | 1 | 2 | 5 | 7 | 8 | 3 | 5 | 7 | |||
2 | 4 | 5 | 6 | 2 | 3 | 5 | 6 | 8 | 4 | 5 | 6 | 7 | 8 | 9 |
1 | 2 | 4 | 6 | 8 | 1 | 2 | 3 | 7 | 8 | 9 | ||||
1 | 2 | 3 | 4 | 7 | 1 | 2 | 3 | 4 | 5 | 6 | ||||
2 | 3 | 5 | 6 | 8 | 9 | |||||||||
1 | 3 | 4 | 6 | 7 | 9 | |||||||||
1 | 2 | 4 | 5 | 7 | 8 | |||||||||
2 | 3 | 4 | 6 | 7 | 8 | |||||||||
1 | 3 | 4 | 5 | 8 | 9 | |||||||||
1 | 2 | 5 | 6 | 7 | 9 | |||||||||
2 | 3 | 4 | 5 | 7 | 9 | |||||||||
1 | 3 | 5 | 6 | 7 | 8 | |||||||||
1 | 2 | 4 | 6 | 8 | 9 | |||||||||
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Verma, A., Jaggi, S., Varghese, E. et al. A Note on the Construction of TORDs Using t-Designs. J Indian Soc Probab Stat (2024). https://doi.org/10.1007/s41096-023-00174-5
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DOI: https://doi.org/10.1007/s41096-023-00174-5