Abstract
Group divisible designs are the most important class of partially balanced incomplete block (PBIB) designs. A list of new group divisible designs with r, k ⩽ 10 is provided.
Keywords: experimental design, group divisible design, partially balanced designs
1. Introduction
Group divisible designs are the most important class of partially balanced incomplete block (PBIB) designs. Clatworthy, Cameron, and Speckman at the National Bureau of Standards [3] tabulated group divisible designs with r, k ≤10. Since then, a good number of new group divisible designs not listed in reference [3] have been reported by various authors in different journals. Here, a list of new group divisible designs not found in the tables in reference [3] is provided.
2. New Group Divisible Designs
Table 1 gives new group divisible designs with r, k ⩽ 10.
Table 1.
New group divisible designs with r, k ⩽ 10.
| No. | v | r | k | b | m | n | λ1 | λ2 | Ea | Sourceb |
|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 16 | 9 | 3 | 48 | 8 | 2 | 4 | 1 | 0.69 | BP[1] |
| 2 | 18 | 10 | 3 | 60 | 9 | 2 | 4 | 1 | 0.69 | F[7] |
| 3 | 12 | 7 | 4 | 21 | 6 | 2 | 1 | 2 | 0.82 | F[7] |
| 4 | 12 | 7 | 4 | 21 | 2 | 6 | 3 | 1 | 0.79 | JT[8] |
| 5 | 12 | 8 | 4 | 24 | 4 | 3 | 3 | 2 | 0.82 | JT[8] |
| 6 | 12 | 9 | 4 | 27 | 2 | 6 | 3 | 2 | 0.82 | JT[8] |
| 7 | 12 | 9 | 4 | 27 | 6 | 2 | 7 | 2 | 0.75 | F[7] |
| 8 | 12 | 10 | 4 | 30 | 6 | 2 | 0 | 3 | 0.81 | F[7] |
| 9 | 14 | 10 | 4 | 35 | 7 | 2 | 6 | 2 | 0.80 | F[7] |
| 10 | 16 | 6 | 4 | 24 | 8 | 2 | 4 | 1 | 0.78 | BP[1] |
| 11 | 18 | 10 | 4 | 45 | 6 | 3 | 0 | 2 | 0.80 | F[7] |
| 12 | 20 | 8 | 4 | 40 | 10 | 2 | 6 | 1 | 0.76 | BP[1] |
| 13 | 22 | 8 | 4 | 44 | 11 | 2 | 2 | 4 | 0.77 | F[7] |
| 14 | 24 | 9 | 4 | 54 | 12 | 2 | 5 | 1 | 0.77 | F[7] |
| 15 | 26 | 10 | 4 | 65 | 13 | 2 | 6 | 1 | 0.76 | F[7] |
| 16 | 14 | 10 | 5 | 28 | 7 | 2 | 4 | 3 | 0.86 | JT[8] |
| 17 | 15 | 8 | 5 | 24 | 3 | 5 | 3 | 2 | 0.86 | JT[8] |
| 18 | 15 | 8 | 5 | 24 | 5 | 3 | 4 | 2 | 0.85 | JT[8] |
| 19 | 15 | 10 | 5 | 30 | 3 | 5 | 5 | 2 | 0.84 | S[10] |
| 20 | 22 | 10 | 5 | 44 | 11 | 2 | 0 | 2 | 0.84 | F[7] |
| 21 | 12 | 7 | 6 | 14 | 6 | 2 | 5 | 3 | 0.91 | JT[8] |
| 22 | 12 | 9 | 6 | 18 | 6 | 2 | 5 | 4 | 0.91 | F[7] |
| 23 | 12 | 9 | 6 | 18 | 3 | 4 | 7 | 3 | 0.89 | BP[2] |
| 24 | 12 | 10 | 6 | 20 | 3 | 4 | 6 | 4 | 0.91 | JT[8] |
| 25 | 16 | 9 | 6 | 24 | 4 | 4 | 7 | 2 | 0.86 | S[10] |
| 26 | 12 | 7 | 7 | 12 | 3 | 4 | 6 | 3 | 0.92 | BP[2] |
| 27 | 16 | 7 | 7 | 16 | 4 | 4 | 2 | 3 | 0.91 | JT[8] |
| 28 | 16 | 7 | 7 | 16 | 8 | 2 | 0 | 3 | 0.91 | D[4] |
| 29 | 21 | 7 | 7 | 21 | 7 | 3 | 3 | 2 | 0.90 | F[7] |
| 30 | 24 | 7 | 7 | 24 | 8 | 3 | 0 | 2 | 0.89 | F[7] |
| 31 | 35 | 7 | 7 | 35 | 7 | 5 | 3 | 1 | 0.87 | F[7] |
| 32 | 45 | 7 | 7 | 45 | 15 | 3 | 0 | 1 | 0.88 | DR[6] |
| 33 | 42 | 8 | 8 | 42 | 7 | 6 | 4 | 1 | 0.88 | F[7] |
| 34 | 16 | 9 | 9 | 16 | 4 | 4 | 4 | 5 | 0.95 | JT[8] |
| 35 | 18 | 10 | 9 | 20 | 3 | 6 | 4 | 5 | 0.79 | JT[8] |
| 36 | 20 | 9 | 9 | 20 | 4 | 5 | 3 | 4 | 0.94 | JT[8] |
| 37 | 20 | 9 | 9 | 20 | 10 | 2 | 0 | 4 | 0.93 | D[4] |
| 38 | 24 | 9 | 9 | 24 | 6 | 4 | 4 | 3 | 0.93 | S[9] |
| 39 | 38 | 9 | 9 | 38 | 19 | 2 | 0 | 2 | 0.91 | DR[6] |
| 40 | 40 | 9 | 9 | 40 | 10 | 4 | 0 | 2 | 0.91 | DN[5] |
| 41 | 49 | 9 | 9 | 49 | 7 | 7 | 5 | 1 | 0.89 | F[7] |
| 42 | 21 | 10 | 10 | 21 | 7 | 3 | 9 | 4 | 0.94 | F[7] |
| 43 | 21 | 10 | 10 | 21 | 3 | 7 | 8 | 3 | 0.93 | BP[2] |
| 44 | 24 | 10 | 10 | 24 | 8 | 3 | 3 | 4 | 0.94 | S[9] |
| 45 | 28 | 10 | 10 | 28 | 7 | 4 | 6 | 3 | 0.93 | F[7] |
| 46 | 56 | 10 | 10 | 56 | 7 | 8 | 6 | 1 | 0.89 | F[7] |
E stands for average efficiency factor.
The abbreviations BP, D, DN, DR, F, JT, and S stand for Bhangwandas and Parihar, Dey, Dey and Nigam, De and Roy, Freeman, John and Turner, and Sinha, respectively.
Biography
About the author: Dr. Kishore Sinha is an Associate Professor in the Department of Statistics, Birsa Agricultural University, Ranchi, India.
3. References
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