Some Series of Resolvable Semi–Regular Group Divisible and Rectangular Designs
10 / 7
Keywords:
Global Decomposable design; Group divisible design; Rectangular design; Difference matrix; Resolvable design. MSC: 62K10; 05B05; 94A62; 94B05Abstract
Here, some series of resolvable global decomposable semi–regular group divisible designs are obtained using difference matrices. A series of
resolvable rectangular designs based on difference matrix is also provided. A table of resolvable rectangular designs under r, k ≤ 10 is also provided.
Downloads
References
1. Clatworthy, W.H. (1973). Tables of two–associate–class partially
2. balanced designs. National Bureau of Standards(U.S.), Applied
3. Mathematics, Series 63.
4. Dawson, J.E. (1985). A construction of generalized Hadamard matrices
5. GH (4q, EA(q)). Discrete Mathematics, 11, 103–110.
6. Dey, A. and Mukerjee, R. (1999). Fractional factorial plans. Wiley
7. Inter–Science, New York.
8. Gupta, S. and Mukerjee, R. (1989). A Calculus for Factorial
9. Arrangements, Lecture Notes in Statistics, Vol. 59, Springer
10. Verlag, New York.
11. Ionin, Y.J. and Shrikhande, M.S. (2006). Decomposable symmetric
12. designs. Discrete Mathematics, 306, 1557–1568.
13. Morgan, J.P., and Reck, B.H.(2007). Resolvable designs with
14. large blocks. The Annals of Statistics, 35(2), 747–771. doi:
15. 10.1214/009053606000001253.
16. Patterson, H.D., and Silvey, V. (1980). Statutory and recommended
17. list trials of crop varities in the United Kingdom. Journal of the
18. Royal Statistical Society: Series A, 143(3), 219–252. doi: 10.
19. 2307/2982128.
20. Pei, D. 2006. A survey of construction for A2–codes. In Authentication
21. codes and combinatorial designs. Discrete mathematics and its
22. applications, ed. K. H. Rosen, 215–230. New York: Chapman &
23. Hall/CRC.
24. Raghavarao, D. and Padgett, Lakshmi V. (2005). Block designs.
25. Analysis, Combinatorics and Applications. Series on Applied
26. Mathematics, 17, World Scientific, Singapore.
27. Saurabh, S. and Sinha, K. (2023a). A list of new partially balanced
28. designs. Communications in Statistics–Theory and Methods,
29. 52(23), 8607–8610.
30. Saurabh, S. and Sinha, K. (2023b). Matrix approaches to constructions
31. of group divisible designs. Bulletin of the ICA, 97, 83–105.
32. Saurabh, S. (2024). Some matrix constructions of non–symmetric
33. regular group divisible designs. Bulletin of the ICA, 102, 129–146.
34. Saurabh, S. (2026a). Combinatorial designs with resolvable subdesigns
35. based on generalized Hadamard matrices. Galois Journal of
36. Algebra, 2(2), 66–73.
37. Saurabh, S. (2026b). Some series of cyclic partially balanced designs.
38. Journal of the Indian Society of Agricultural Statistics, 80(2),
39. 389–394.
40. Saurabh, S. (2026c). Some combinatorial applications of tactical
41. decomposable rectangular designs families. Utilitas Mathematica,
42. 128, 441–456.
43. Singh, M.K. and Saurabh, S. (2023). On certain classes of rectangular
44. designs. Calcutta Statistical Association Bulletin, 75(1), 72–96.
45. Sinha, K., Singh, M.K., Kagyeyama. S. and Singh, R.S. (2002). Some
46. series of rectangular designs. Journal of Statistical Planning and
47. Inference, 105, 39–46.
48. Suen, C. (1989). Some rectangular designs constructed by the method
49. of differences. Journal of Statistical Planning and Inference, 21,
50. 273–276.
51. Xu, H., Feng, D., Sun, C. and Bai, B. (2015). Construction of LDPC
52. codes based on resolvable group divisible designs. In International
53. Workshop on High Mobility Wireless Communications (HMWC),
54. China, October 21–23. p. 111–115.
55. Xu, H., Yu, Z., Feng, D. and Zhu, H. (2020). New construction of
56. partial geometries based on group divisible designs and their
57. associated LDPC codes. Physical Communication, 39, 100970.
58. doi: 10.1016/j.phycom.2019.100970