Composite construction of group divisible designs. (English) Zbl 0691.62072
Summary: Two new methods of constructing group divisible designs are given. In particular, a new resolvable solution for the SR 39 is presented.
Keywords:
BIB design; non-isomorphic; regular; 2-associate partially balanced incomplete block designs; methods of constructing group divisible designs; resolvable; SR 39References:
| [1] | Banerjee, S. and Kageyama, S. (1986). A method of constructing regular block designs, J. Statist. Plann. Inference, 13, 399-401. · Zbl 0592.62069 · doi:10.1016/0378-3758(86)90150-3 |
| [2] | Banerjee, S., Bhagwandas and Kageyama, S. (1985a). Some constructions of PBIB designs, Ann. Inst. Statist. Math., 37, 145-150. · Zbl 0577.62070 · doi:10.1007/BF02481087 |
| [3] | Banerjee, S., Bhagwandas and Kageyama, S. (1985b). On the duals of contractions of t-(v,k,?t) designs, Sankhy? Ser. B, 47, 432-435. · Zbl 0593.62072 |
| [4] | Bhagwandas and Parihar, J. S. (1982). Some new series of regular group divisible designs, Comm. Statist. A?Theory Methods, 11, 761-768. · Zbl 0512.62078 |
| [5] | Bhagwandas, Banerjee, S. and Kageyama, S. (1985). Patterned constructions of partially balanced incomplete block designs, Comm. Statist. A?Theory Methods, 14, 1259-1267. · Zbl 0574.62072 · doi:10.1080/03610928508828974 |
| [6] | Cheng, C. S. (1981). On the comparison of PBIB designs with two associate classes, Ann. Inst. Statist. Math., 33, 155-164. · Zbl 0483.62065 · doi:10.1007/BF02480929 |
| [7] | Clatworthy, W. H. (1973). Tables of two-associate-class partially balanced designs, NBS Applied Mathematics Series, 63, U.S. Department of Commerce, National Bureau of Standards, Washington, D.C. · Zbl 0289.05017 |
| [8] | Dey, A. and Nigam, A. K. (1985). Construction of group divisible designs, J. Indian Soc. Agricultural Statist., 37, 163-166. |
| [9] | Freeman, G. H. (1976). A cyclic method of constructing regular group divisible incomplete block designs, Biometrika, 63, 555-558. · Zbl 0344.62065 · doi:10.1093/biomet/63.3.555 |
| [10] | Hanani, H. (1975). Balanced incomplete block designs and related designs, Discrete Math., 11, 255-369. · Zbl 0361.62067 · doi:10.1016/0012-365X(75)90040-0 |
| [11] | Kageyama, S. (1985a). A structural classification of semi-regular group divisible designs, Statist. Probab. Lett., 3, 25-27. · Zbl 0562.62063 · doi:10.1016/0167-7152(85)90007-0 |
| [12] | Kageyama, S. (1985b). A construction of group divisible designs, J. Statist. Plann. Inference, 12, 123-125. · Zbl 0572.05012 · doi:10.1016/0378-3758(85)90060-6 |
| [13] | Kageyama, S. and Mohan, R. N. (1985a). Three methods of constructing PBIB designs, Comm. Statist. A?Theory Methods, 13, 3185-3189 (Correction: ibid. (1987). 16, 2793). · Zbl 0576.62079 · doi:10.1080/03610928408828886 |
| [14] | Kageyama, S. and Mohan, R. N. (1985b). On a construction of group divisible partially balanced incomplete block designs, Sankhy? Ser. B, 47, 292-293. |
| [15] | Kageyama, S. and Tanaka, T. (1981). Some families of group divisible designs, J. Statist. Plann. Inference, 5, 231-241. · Zbl 0506.62059 · doi:10.1016/0378-3758(81)90003-3 |
| [16] | Sinha, K. (1987). A method of construction of regular group divisible designs, Biometrika, 74, 443-444. · Zbl 0618.62080 · doi:10.1093/biomet/74.2.443 |
| [17] | Sinha, K. and Kageyama, S. (1986). Pairwise balanced semi-regular and regular group divisible designs, Bull. Inform. Cybernet., 22, 55-57. · Zbl 0599.62091 |
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