Optimal orthogonal arrays
One this page we present orthognal arrays that can be used to analyse second-order interactions. We have selected the arrays that have good D-efficiency. A more detailed description of the software and methods used to obtain the results can be found in the paper Two-level designs to estimate all main effects and two-factor interactions. Note that for small D-efficiency values (corresponding to small A-efficiency values and large average VIF values) numerical instabilities may occur.
For more information please contact pieter.eendebak@gmail.com
Software for manipulating the arrays can be found here. If you use these data, please cite the paper Two-level designs to estimate all main effects and two-factor interactions.
Strength 2
Strength 2, 100 runs
Maximal number of factors from rank constraints: 13.
| Case | Isomorphisms (full rank) | Best D-efficiency | Best average VIF | Data | Best GWLP |
| OA(100; 2; 23) | 13 (12) | 0.9993 | 1.0014 | all arrays | 1.0000,0.0000,0.0000,0.0016 |
| OA(100; 2; 24) | 523 (523) | 0.9978 | 1.0044 | all arrays (binary) | 1.0000,0.0000,0.0000,0.0064,0.0016 |
Strength 2, 104 runs
Maximal number of factors from rank constraints: 13.
| Case | Isomorphisms (full rank) | Best D-efficiency | Best average VIF | Data | Best GWLP |
| OA(104; 2; 23) | 14 (13) | 1.0000 | 1.0000 | all arrays | 1.0000,0.0000,0.0000,0.0000 |
| OA(104; 2; 24) | 694 (692) | 0.9984 | 1.0032 | all arrays (binary) | 1.0000,0.0000,0.0000,0.0000,0.0059 |
Strength 2, 108 runs
Maximal number of factors from rank constraints: 14.
| Case | Isomorphisms (full rank) | Best D-efficiency | Best average VIF | Data | Best GWLP |
| OA(108; 2; 23) | 14 (13) | 0.9994 | 1.0012 | all arrays | 1.0000,0.0000,0.0000,0.0014 |
| OA(108; 2; 24) | 709 (709) | 0.9981 | 1.0038 | all arrays (binary) | 1.0000,0.0000,0.0000,0.0055,0.0014 |
Strength 2, 112 runs
Maximal number of factors from rank constraints: 14.
| Case | Isomorphisms (full rank) | Best D-efficiency | Best average VIF | Data | Best GWLP |
| OA(112; 2; 23) | 15 (14) | 1.0000 | 1.0000 | all arrays | 1.0000,0.0000,0.0000,0.0000 |
| OA(112; 2; 24) | 919 (917) | 1.0000 | 1.0000 | all arrays (binary) | 1.0000,0.0000,0.0000,0.0000,0.0000 |
Strength 2, 116 runs
Maximal number of factors from rank constraints: 14.
| Case | Isomorphisms (full rank) | Best D-efficiency | Best average VIF | Data | Best GWLP |
| OA(116; 2; 23) | 15 (14) | 0.9995 | 1.0010 | all arrays | 1.0000,0.0000,0.0000,0.0012 |
| OA(116; 2; 24) | 943 (943) | 0.9984 | 1.0033 | all arrays (binary) | 1.0000,0.0000,0.0000,0.0048,0.0012 |
Strength 2, 12 runs
Maximal number of factors from rank constraints: 4.
| Case | Isomorphisms (full rank) | Best D-efficiency | Best average VIF | Data | Best GWLP |
| OA(12; 2; 23) | 2 (1) | 0.9508 | 1.1071 | all arrays | 1.0000,0.0000,0.0000,0.1111 |
| OA(12; 2; 24) | 1 (1) | 0.8141 | 1.5682 | all arrays | 1.0000,0.0000,0.0000,0.4444,0.1111 |
Strength 2, 120 runs
Maximal number of factors from rank constraints: 14.
| Case | Isomorphisms (full rank) | Best D-efficiency | Best average VIF | Data | Best GWLP |
| OA(120; 2; 23) | 16 (15) | 1.0000 | 1.0000 | all arrays | 1.0000,0.0000,0.0000,0.0000 |
| OA(120; 2; 24) | 1198 (1196) | 0.9988 | 1.0024 | all arrays (binary) | 1.0000,0.0000,0.0000,0.0000,0.0044 |
Strength 2, 124 runs
Maximal number of factors from rank constraints: 15.
| Case | Isomorphisms (full rank) | Best D-efficiency | Best average VIF | Data | Best GWLP |
| OA(124; 2; 23) | 16 (15) | 0.9996 | 1.0009 | all arrays | 1.0000,0.0000,0.0000,0.0010 |
| OA(124; 2; 24) | 1234 (1234) | 0.9986 | 1.0029 | all arrays (binary) | 1.0000,0.0000,0.0000,0.0042,0.0010 |
Strength 2, 128 runs
Maximal number of factors from rank constraints: 15.
| Case | Isomorphisms (full rank) | Best D-efficiency | Best average VIF | Data | Best GWLP |
| OA(128; 2; 23) | 17 (16) | 1.0000 | 1.0000 | all arrays | 1.0000,0.0000,0.0000,0.0039 |
| OA(128; 2; 24) | 1543 (1541) | 1.0000 | 1.0000 | all arrays (binary) | 1.0000,0.0000,0.0000,0.0000,0.0000 |
Strength 2, 16 runs
Maximal number of factors from rank constraints: 5.
| Case | Isomorphisms (full rank) | Best D-efficiency | Best average VIF | Data | Best GWLP |
| OA(16; 2; 23) | 3 (2) | 1.0000 | 1.0000 | all arrays | 1.0000,0.0000,0.0000,0.0000 |
| OA(16; 2; 24) | 5 (3) | 1.0000 | 1.0000 | all arrays | 1.0000,0.0000,0.0000,0.0000,0.0000 |
| OA(16; 2; 25) | 11 (3) | 1.0000 | 1.0000 | all arrays | 1.0000,0.0000,0.0000,0.0000,0.0000,1.0000 |
Strength 2, 20 runs
Maximal number of factors from rank constraints: 5.
| Case | Isomorphisms (full rank) | Best D-efficiency | Best average VIF | Data | Best GWLP |
| OA(20; 2; 23) | 3 (2) | 0.9827 | 1.0357 | all arrays | 1.0000,0.0000,0.0000,0.0400 |
| OA(20; 2; 24) | 3 (3) | 0.9395 | 1.1461 | all arrays | 1.0000,0.0000,0.0000,0.1600,0.0400 |
| OA(20; 2; 25) | 11 (4) | 0.8661 | 1.3646 | all arrays | 1.0000,0.0000,0.0000,0.4000,0.2000,0.0000 |
Strength 2, 24 runs
Maximal number of factors from rank constraints: 6.
| Case | Isomorphisms (full rank) | Best D-efficiency | Best average VIF | Data | Best GWLP |
| OA(24; 2; 23) | 4 (3) | 1.0000 | 1.0000 | all arrays | 1.0000,0.0000,0.0000,0.0000 |
| OA(24; 2; 24) | 10 (8) | 0.9684 | 1.0682 | all arrays | 1.0000,0.0000,0.0000,0.0000,0.1111 |
| OA(24; 2; 25) | 63 (36) | 0.9390 | 1.1313 | all arrays | 1.0000,0.0000,0.0000,0.0000,0.5556,0.0000 |
| OA(24; 2; 26) | 1350 (447) | 0.7926 | 2.0376 | all arrays (binary) | 1.0000,0.0000,0.0000,0.0000,1.6667,0.0000,0.0000 |
Strength 2, 28 runs
Maximal number of factors from rank constraints: 6.
| Case | Isomorphisms (full rank) | Best D-efficiency | Best average VIF | Data | Best GWLP |
| OA(28; 2; 23) | 4 (3) | 0.9912 | 1.0179 | all arrays | 1.0000,0.0000,0.0000,0.0204 |
| OA(28; 2; 24) | 7 (7) | 0.9712 | 1.0614 | all arrays | 1.0000,0.0000,0.0000,0.0816,0.0204 |
| OA(28; 2; 25) | 127 (105) | 0.9409 | 1.1319 | all arrays (binary) | 1.0000,0.0000,0.0000,0.2041,0.1020,0.0000 |
| OA(28; 2; 26) | 17826 (14221) | 0.8855 | 1.3053 | all arrays (binary) | 1.0000,0.0000,0.0000,0.4082,0.3061,0.0000,0.7347 |
Strength 2, 32 runs
Maximal number of factors from rank constraints: 7.
| Case | Isomorphisms (full rank) | Best D-efficiency | Best average VIF | Data | Best GWLP |
| OA(32; 2; 23) | 5 (4) | 1.0000 | 1.0000 | all arrays | 1.0000,0.0000,0.0000,0.0000 |
| OA(32; 2; 24) | 19 (17) | 1.0000 | 1.0000 | all arrays | 1.0000,0.0000,0.0000,0.0000,0.0000 |
| OA(32; 2; 25) | 491 (429) | 1.0000 | 1.0000 | all arrays (binary) | 1.0000,0.0000,0.0000,0.0000,0.0000,0.0000 |
| OA(32; 2; 26) | 266217 (246813) | 1.0000 | 1.0000 | 2000 arrays (binary) | 1.0000,0.0000,0.0000,0.0000,0.0000,0.0000,1.0000 |
| OA(32; 2; 27) | ~ 1010 (≥ 988) | 0.8432 ≤ D ≤ 0.8648 | ≤ 1.5135 | 100 array(s) (binary) | - |
| OA(32; 2; 27) | ~ 1010 (≥ 15) | 0.8432 ≤ D ≤ 0.8799 | ≤ 1.5135 | 15 array(s) | - |
| OA(32; 2; 27) | 530469996 (395932754) | 0.8432 | 1.37159375 | - | - |
Strength 2, 36 runs
Maximal number of factors from rank constraints: 7.
| Case | Isomorphisms (full rank) | Best D-efficiency | Best average VIF | Data | Best GWLP |
| OA(36; 2; 23) | 5 (4) | 0.9947 | 1.0107 | all arrays | 1.0000,0.0000,0.0000,0.0123 |
| OA(36; 2; 24) | 15 (15) | 0.9827 | 1.0362 | all arrays | 1.0000,0.0000,0.0000,0.0494,0.0123 |
| OA(36; 2; 25) | 1242 (1174) | 0.9635 | 1.0800 | all arrays (binary) | 1.0000,0.0000,0.0000,0.1235,0.0617,0.0000 |
| OA(36; 2; 26) | ~ 3 ⋅ 106 (≥ 125990) | 0.9374 | ≤ 1.1432 | 200 array(s) (binary) | - |
| OA(36; 2; 26) | ~ 3 ⋅ 106 (≥ 2777) | 0.9374 | ≤ 1.1432 | 200 array(s) (binary) | - |
| OA(36; 2; 27) | ~ 1010 (≥ 9254) | 0.9022 | ≤ 1.2414 | 100 array(s) (binary) | - |
Strength 2, 40 runs
Maximal number of factors from rank constraints: 8.
| Case | Isomorphisms (full rank) | Best D-efficiency | Best average VIF | Data | Best GWLP |
| OA(40; 2; 23) | 6 (5) | 1.0000 | 1.0000 | all arrays | 1.0000,0.0000,0.0000,0.0000 |
| OA(40; 2; 24) | 32 (30) | 0.9889 | 1.0227 | all arrays | 1.0000,0.0000,0.0000,0.0000,0.0400 |
| OA(40; 2; 25) | 3919 (3786) | 0.9781 | 1.0446 | all arrays (binary) | 1.0000,0.0000,0.0000,0.0000,0.2000,0.0000 |
| OA(40; 2; 26) | ~ 107 (≥ 6947816) | 0.9657 | ≤ 1.0682 | 200 array(s) (binary) | - |
| OA(40; 2; 27) | ~ 1012 (≥ 2860032) | 0.9245 ≤ D ≤ 0.9414 | ≤ 1.1727 | 200 array(s) (binary) | - |
| OA(40; 2; 28) | ~ 1016 (≥ 70) | 0.8019 ≤ D ≤ 0.9506 | ≤ 1.7947 | 70 array(s) | - |
Strength 2, 44 runs
Maximal number of factors from rank constraints: 8.
| Case | Isomorphisms (full rank) | Best D-efficiency | Best average VIF | Data | Best GWLP |
| OA(44; 2; 23) | 6 (5) | 0.9964 | 1.0071 | all arrays | 1.0000,0.0000,0.0000,0.0083 |
| OA(44; 2; 24) | 28 (28) | 0.9886 | 1.0234 | all arrays | 1.0000,0.0000,0.0000,0.0331,0.0083 |
| OA(44; 2; 25) | 10151 (10008) | 0.9769 | 1.0483 | all arrays (binary) | 1.0000,0.0000,0.0000,0.0826,0.0413,0.0000 |
| OA(44; 2; 26) | ~ 3 ⋅ 108 (≥ 2046270) | 0.9622 | ≤ 1.0787 | 30 array(s) | - |
| OA(44; 2; 27) | ~ 1014 (≥ 121293) | 0.9449 ≤ D ≤ 0.9531 | ≤ 1.1238 | 100 array(s) (binary) | - |
| OA(44; 2; 28) | ~ 1019 (≥ 7618) | 0.8524 ≤ D ≤ 0.9567 | ≤ 1.4549 | 100 array(s) (binary) | - |
Strength 2, 48 runs
Maximal number of factors from rank constraints: 9.
| Case | Isomorphisms (full rank) | Best D-efficiency | Best average VIF | Data | Best GWLP |
| OA(48; 2; 23) | 7 (6) | 1.0000 | 1.0000 | all arrays | 1.0000,0.0000,0.0000,0.0000 |
| OA(48; 2; 24) | 54 (52) | 1.0000 | 1.0000 | all arrays | 1.0000,0.0000,0.0000,0.0000,0.0000 |
| OA(48; 2; 25) | 27878 (27601) | 1.0000 | 1.0000 | 2000 arrays (binary) | 1.0000,0.0000,0.0000,0.0000,0.0000,0.1111 |
| OA(48; 2; 26) | » 109 (≥ 688987) | 0.9841 | ≤ 1.0341 | 8 array(s) | - |
| OA(48; 2; 27) | » 1014 (≥ 154) | 0.9585 ≤ D ≤ 0.9787 | ≤ 1.1034 | 12 array(s) | - |
| OA(48; 2; 28) | » 1019 (≥ 1) | 0.8202 ≤ D ≤ 0.9832 | ≤ 1.7349 | 1 array(s) | - |
Strength 2, 52 runs
Maximal number of factors from rank constraints: 9.
| Case | Isomorphisms (full rank) | Best D-efficiency | Best average VIF | Data | Best GWLP |
| OA(52; 2; 23) | 7 (6) | 0.9975 | 1.0051 | all arrays | 1.0000,0.0000,0.0000,0.0059 |
| OA(52; 2; 24) | 48 (48) | 0.9918 | 1.0167 | all arrays | 1.0000,0.0000,0.0000,0.0237,0.0059 |
| OA(52; 2; 25) | 68555 (68272) | 0.9830 | 1.0354 | 2000 arrays (binary) | 1.0000,0.0000,0.0000,0.0592,0.0296,0.0000 |
| OA(52; 2; 26) | » 108 (≥ 235305) | 0.9711 ≤ D ≤ 0.9731 | ≤ 1.0614 | 20 array(s) | - |
Strength 2, 56 runs
Maximal number of factors from rank constraints: 10.
| Case | Isomorphisms (full rank) | Best D-efficiency | Best average VIF | Data | Best GWLP |
| OA(56; 2; 23) | 8 (7) | 1.0000 | 1.0000 | all arrays | 1.0000,0.0000,0.0000,0.0000 |
| OA(56; 2; 24) | 84 (82) | 0.9944 | 1.0114 | all arrays | 1.0000,0.0000,0.0000,0.0000,0.0204 |
| OA(56; 2; 25) | 168146 (167667) | 0.9888 | 1.0226 | 2000 arrays (binary) | 1.0000,0.0000,0.0000,0.0000,0.1020,0.0000 |
Strength 2, 60 runs
Maximal number of factors from rank constraints: 10.
| Case | Isomorphisms (full rank) | Best D-efficiency | Best average VIF | Data | Best GWLP |
| OA(60; 2; 23) | 8 (7) | 0.9981 | 1.0038 | all arrays | 1.0000,0.0000,0.0000,0.0044 |
| OA(60; 2; 24) | 79 (79) | 0.9939 | 1.0124 | all arrays | 1.0000,0.0000,0.0000,0.0178,0.0044 |
| OA(60; 2; 25) | 385693 (385160) | 0.9877 | 1.0251 | 2000 arrays (binary) | 1.0000,0.0000,0.0000,0.0444,0.0222,0.0000 |
Strength 2, 64 runs
Maximal number of factors from rank constraints: 10.
| Case | Isomorphisms (full rank) | Best D-efficiency | Best average VIF | Data | Best GWLP |
| OA(64; 2; 23) | 9 (8) | 1.0000 | 1.0000 | all arrays | 1.0000,0.0000,0.0000,0.0000 |
| OA(64; 2; 24) | 128 (126) | 1.0000 | 1.0000 | all arrays (binary) | 1.0000,0.0000,0.0000,0.0000,0.0000 |
Strength 2, 68 runs
Maximal number of factors from rank constraints: 11.
| Case | Isomorphisms (full rank) | Best D-efficiency | Best average VIF | Data | Best GWLP |
| OA(68; 2; 23) | 9 (8) | 0.9985 | 1.0030 | all arrays | 1.0000,0.0000,0.0000,0.0035 |
| OA(68; 2; 24) | 123 (123) | 0.9952 | 1.0096 | all arrays (binary) | 1.0000,0.0000,0.0000,0.0138,0.0035 |
Strength 2, 72 runs
Maximal number of factors from rank constraints: 11.
| Case | Isomorphisms (full rank) | Best D-efficiency | Best average VIF | Data | Best GWLP |
| OA(72; 2; 23) | 10 (9) | 1.0000 | 1.0000 | all arrays | 1.0000,0.0000,0.0000,0.0000 |
| OA(72; 2; 24) | 188 (186) | 0.9966 | 1.0068 | all arrays (binary) | 1.0000,0.0000,0.0000,0.0000,0.0123 |
Strength 2, 76 runs
Maximal number of factors from rank constraints: 11.
| Case | Isomorphisms (full rank) | Best D-efficiency | Best average VIF | Data | Best GWLP |
| OA(76; 2; 23) | 10 (9) | 0.9988 | 1.0024 | all arrays | 1.0000,0.0000,0.0000,0.0028 |
| OA(76; 2; 24) | 184 (184) | 0.9962 | 1.0077 | all arrays (binary) | 1.0000,0.0000,0.0000,0.0111,0.0028 |
Strength 2, 80 runs
Maximal number of factors from rank constraints: 12.
| Case | Isomorphisms (full rank) | Best D-efficiency | Best average VIF | Data | Best GWLP |
| OA(80; 2; 23) | 11 (10) | 1.0000 | 1.0000 | all arrays | 1.0000,0.0000,0.0000,0.0000 |
| OA(80; 2; 24) | 270 (268) | 1.0000 | 1.0000 | all arrays (binary) | 1.0000,0.0000,0.0000,0.0000,0.0000 |
Strength 2, 84 runs
Maximal number of factors from rank constraints: 12.
| Case | Isomorphisms (full rank) | Best D-efficiency | Best average VIF | Data | Best GWLP |
| OA(84; 2; 23) | 11 (10) | 0.9990 | 1.0019 | all arrays | 1.0000,0.0000,0.0000,0.0023 |
| OA(84; 2; 24) | 268 (268) | 0.9969 | 1.0063 | all arrays (binary) | 1.0000,0.0000,0.0000,0.0091,0.0023 |
Strength 2, 88 runs
Maximal number of factors from rank constraints: 12.
| Case | Isomorphisms (full rank) | Best D-efficiency | Best average VIF | Data | Best GWLP |
| OA(88; 2; 23) | 12 (11) | 1.0000 | 1.0000 | all arrays | 1.0000,0.0000,0.0000,0.0000 |
| OA(88; 2; 24) | 376 (374) | 0.9977 | 1.0045 | all arrays (binary) | 1.0000,0.0000,0.0000,0.0000,0.0083 |
Strength 2, 92 runs
Maximal number of factors from rank constraints: 13.
| Case | Isomorphisms (full rank) | Best D-efficiency | Best average VIF | Data | Best GWLP |
| OA(92; 2; 23) | 12 (11) | 0.9992 | 1.0016 | all arrays | 1.0000,0.0000,0.0000,0.0019 |
| OA(92; 2; 24) | 379 (379) | 0.9974 | 1.0052 | all arrays (binary) | 1.0000,0.0000,0.0000,0.0076,0.0019 |
Strength 2, 96 runs
Maximal number of factors from rank constraints: 13.
| Case | Isomorphisms (full rank) | Best D-efficiency | Best average VIF | Data | Best GWLP |
| OA(96; 2; 23) | 13 (12) | 1.0000 | 1.0000 | all arrays | 1.0000,0.0000,0.0000,0.0000 |
| OA(96; 2; 24) | 517 (515) | 1.0000 | 1.0000 | all arrays (binary) | 1.0000,0.0000,0.0000,0.0000,0.0000 |
Strength 3
Strength 3, 104 runs
Maximal number of factors from rank constraints: 13.
| Case | Isomorphisms (full rank) | Best D-efficiency | Best average VIF | Data | Best GWLP |
| OA(104; 3; 24) | 7 (6) | 0.9984 | 1.0032 | all arrays | 1.0000,0.0000,0.0000,0.0000,0.0059 |
| OA(104; 3; 25) | 49 (49) | 0.9944 | 1.0114 | all arrays | 1.0000,0.0000,0.0000,0.0000,0.0296,0.0000 |
Strength 3, 112 runs
Maximal number of factors from rank constraints: 14.
| Case | Isomorphisms (full rank) | Best D-efficiency | Best average VIF | Data | Best GWLP |
| OA(112; 3; 24) | 8 (7) | 1.0000 | 1.0000 | all arrays | 1.0000,0.0000,0.0000,0.0000,0.0000 |
| OA(112; 3; 25) | 89 (88) | 1.0000 | 1.0000 | all arrays | 1.0000,0.0000,0.0000,0.0000,0.0000,0.0204 |
Strength 3, 120 runs
Maximal number of factors from rank constraints: 14.
| Case | Isomorphisms (full rank) | Best D-efficiency | Best average VIF | Data | Best GWLP |
| OA(120; 3; 24) | 8 (7) | 0.9988 | 1.0024 | all arrays | 1.0000,0.0000,0.0000,0.0000,0.0044 |
| OA(120; 3; 25) | 82 (82) | 0.9958 | 1.0085 | all arrays | 1.0000,0.0000,0.0000,0.0000,0.0222,0.0000 |
Strength 3, 128 runs
Maximal number of factors from rank constraints: 15.
| Case | Isomorphisms (full rank) | Best D-efficiency | Best average VIF | Data | Best GWLP |
| OA(128; 3; 24) | 9 (8) | 1.0000 | 1.0000 | all arrays | 1.0000,0.0000,0.0000,0.0000,0.0000 |
| OA(128; 3; 25) | 138 (137) | 1.0000 | 1.0000 | all arrays (binary) | 1.0000,0.0000,0.0000,0.0000,0.0000,0.0000 |
Strength 3, 16 runs
Maximal number of factors from rank constraints: 5.
| Case | Isomorphisms (full rank) | Best D-efficiency | Best average VIF | Data | Best GWLP |
| OA(16; 3; 24) | 2 (1) | 1.0000 | 1.0000 | all arrays | 1.0000,0.0000,0.0000,0.0000,0.0000 |
| OA(16; 3; 25) | 2 (1) | 1.0000 | 1.0000 | all arrays | 1.0000,0.0000,0.0000,0.0000,0.0000,1.0000 |
Strength 3, 24 runs
Maximal number of factors from rank constraints: 6.
| Case | Isomorphisms (full rank) | Best D-efficiency | Best average VIF | Data | Best GWLP |
| OA(24; 3; 24) | 2 (1) | 0.9684 | 1.0682 | all arrays | 1.0000,0.0000,0.0000,0.0000,0.1111 |
| OA(24; 3; 25) | 1 (1) | 0.8681 | 1.3906 | all arrays | 1.0000,0.0000,0.0000,0.0000,0.5556,0.0000 |
| OA(24; 3; 26) | 2 (0) | 0.0000 | inf | all arrays | 1.0000,0.0000,0.0000,0.0000,1.6667,0.0000,0.0000 |
Strength 3, 32 runs
Maximal number of factors from rank constraints: 7.
| Case | Isomorphisms (full rank) | Best D-efficiency | Best average VIF | Data | Best GWLP |
| OA(32; 3; 24) | 3 (2) | 1.0000 | 1.0000 | all arrays | 1.0000,0.0000,0.0000,0.0000,0.0000 |
| OA(32; 3; 25) | 5 (4) | 1.0000 | 1.0000 | all arrays | 1.0000,0.0000,0.0000,0.0000,0.0000,0.0000 |
| OA(32; 3; 26) | 10 (5) | 1.0000 | 1.0000 | all arrays | 1.0000,0.0000,0.0000,0.0000,0.0000,0.0000,1.0000 |
| OA(32; 3; 27) | 17 (0) | 0.0000 | inf | all arrays | 1.0000,0.0000,0.0000,0.0000,1.0000,2.0000,0.0000,0.0000 |
Strength 3, 40 runs
Maximal number of factors from rank constraints: 8.
| Case | Isomorphisms (full rank) | Best D-efficiency | Best average VIF | Data | Best GWLP |
| OA(40; 3; 24) | 3 (2) | 0.9889 | 1.0227 | all arrays | 1.0000,0.0000,0.0000,0.0000,0.0400 |
| OA(40; 3; 25) | 3 (3) | 0.9595 | 1.0911 | all arrays | 1.0000,0.0000,0.0000,0.0000,0.2000,0.0000 |
| OA(40; 3; 26) | 9 (4) | 0.9007 | 1.2652 | all arrays | 1.0000,0.0000,0.0000,0.0000,0.6000,0.0000,0.0000 |
| OA(40; 3; 27) | 25 (1) | 0.8030 | 1.8913 | all arrays | 1.0000,0.0000,0.0000,0.0000,1.4000,0.0000,0.8000,0.0000 |
| OA(40; 3; 28) | 105 (0) | 0.0000 | inf | all arrays (binary) | 1.0000,0.0000,0.0000,0.0000,2.8000,2.5600,0.6400,0.0000,0.0400 |
Strength 3, 48 runs
Maximal number of factors from rank constraints: 9.
| Case | Isomorphisms (full rank) | Best D-efficiency | Best average VIF | Data | Best GWLP |
| OA(48; 3; 24) | 4 (3) | 1.0000 | 1.0000 | all arrays | 1.0000,0.0000,0.0000,0.0000,0.0000 |
| OA(48; 3; 25) | 10 (9) | 1.0000 | 1.0000 | all arrays | 1.0000,0.0000,0.0000,0.0000,0.0000,0.1111 |
| OA(48; 3; 26) | 45 (28) | 0.9841 | 1.0341 | all arrays | 1.0000,0.0000,0.0000,0.0000,0.1111,0.4444,0.0000 |
| OA(48; 3; 27) | 397 (178) | 0.9585 | 1.1034 | all arrays (binary) | 1.0000,0.0000,0.0000,0.0000,0.3333,1.3333,0.0000,0.0000 |
| OA(48; 3; 28) | 8383 (43) | 0.8365 | 1.5101 | all arrays (binary) | 1.0000,0.0000,0.0000,0.0000,1.0000,2.6667,0.6667,0.0000,0.0000 |
| OA(48; 3; 29) | 166081 (1) | 0.6753 | 5.6543 | 2000 arrays (binary) | 1.0000,0.0000,0.0000,0.0000,2.4444,5.3333,1.7778,0.0000,0.1111,0.0000 |
Strength 3, 56 runs
Maximal number of factors from rank constraints: 10.
| Case | Isomorphisms (full rank) | Best D-efficiency | Best average VIF | Data | Best GWLP |
| OA(56; 3; 24) | 4 (3) | 0.9944 | 1.0114 | all arrays | 1.0000,0.0000,0.0000,0.0000,0.0204 |
| OA(56; 3; 25) | 7 (7) | 0.9801 | 1.0422 | all arrays | 1.0000,0.0000,0.0000,0.0000,0.1020,0.0000 |
| OA(56; 3; 26) | 86 (74) | 0.9567 | 1.0960 | all arrays | 1.0000,0.0000,0.0000,0.0000,0.3061,0.0000,0.0000 |
| OA(56; 3; 27) | 4049 (3387) | 0.9192 | 1.2012 | all arrays (binary) | 1.0000,0.0000,0.0000,0.0000,0.7143,0.0000,0.5714,0.0000 |
| OA(56; 3; 28) | 757190 (10491) | 0.8642 | 1.4100 | 2000 arrays (binary) | 1.0000,0.0000,0.0000,0.0000,1.4286,0.9796,1.1429,0.0000,0.0204 |
| OA(56; 3; 28) | ~ 106 (10491) | 0.8642 | 1.4100 | 200 array(s) (binary) | - |
| OA(56; 3; 29) | ~ 108 (28) | 0.7610 | 1.9479 | 28 array(s) | - |
| OA(56; 3; 210) | ~ 1010 (0) | 0.0000 | inf | 0 array(s) | - |
Strength 3, 64 runs
Maximal number of factors from rank constraints: 10.
| Case | Isomorphisms (full rank) | Best D-efficiency | Best average VIF | Data | Best GWLP |
| OA(64; 3; 24) | 5 (4) | 1.0000 | 1.0000 | all arrays | 1.0000,0.0000,0.0000,0.0000,0.0000 |
| OA(64; 3; 25) | 19 (18) | 1.0000 | 1.0000 | all arrays | 1.0000,0.0000,0.0000,0.0000,0.0000,0.0000 |
| OA(64; 3; 26) | 358 (326) | 1.0000 | 1.0000 | all arrays (binary) | 1.0000,0.0000,0.0000,0.0000,0.0000,0.0000,0.0000 |
| OA(64; 3; 27) | 91789 (88129) | 1.0000 | 1.0000 | 2000 arrays (binary) | 1.0000,0.0000,0.0000,0.0000,0.0000,0.0000,0.0000,1.0000 |
| OA(64; 3; 28) | ~ 107 (≥ 11335) | 1.0000 | ≤ 1.0000 | 200 array(s) (binary) | - |
| OA(64; 3; 29) | ~ 1011 (≥ 2229) | 0.9254 ≤ D ≤ 0.9626 | ≤ 1.1872 | 200 array(s) (binary) | - |
| OA(64; 3; 210) | ~ 1014 (≥ 33) | 0.8247 ≤ D ≤ 0.9692 | ≤ 1.5476 | 52 array(s) | - |
Strength 3, 72 runs
Maximal number of factors from rank constraints: 11.
| Case | Isomorphisms (full rank) | Best D-efficiency | Best average VIF | Data | Best GWLP |
| OA(72; 3; 24) | 5 (4) | 0.9966 | 1.0068 | all arrays | 1.0000,0.0000,0.0000,0.0000,0.0123 |
| OA(72; 3; 25) | 15 (15) | 0.9881 | 1.0246 | all arrays | 1.0000,0.0000,0.0000,0.0000,0.0617,0.0000 |
| OA(72; 3; 26) | 906 (872) | 0.9745 | 1.0542 | all arrays (binary) | 1.0000,0.0000,0.0000,0.0000,0.1852,0.0000,0.0000 |
| OA(72; 3; 27) | ~ 2 ⋅ 106 (≥ 2137154) | 0.9553 | ≤ 1.0993 | 180 array(s) (binary) | - |
| OA(72; 3; 28) | ~ 109 (≥ 10609) | 0.9283 ≤ D ≤ 0.9439 | ≤ 1.1707 | 200 array(s) (binary) | - |
| OA(72; 3; 29) | ~ 1013 (≥ 5) | 0.8818 ≤ D ≤ 0.9390 | ≤ 1.3474 | 5 array(s) | - |
| OA(72; 3; 210) | ~ 1016 (≥ 0) | 0.0000 ≤ D ≤ 0.9369 | ≤ inf | 0 array(s) | - |
Strength 3, 80 runs
Maximal number of factors from rank constraints: 12.
| Case | Isomorphisms (full rank) | Best D-efficiency | Best average VIF | Data | Best GWLP |
| OA(80; 3; 24) | 6 (5) | 1.0000 | 1.0000 | all arrays | 1.0000,0.0000,0.0000,0.0000,0.0000 |
| OA(80; 3; 25) | 33 (32) | 1.0000 | 1.0000 | all arrays | 1.0000,0.0000,0.0000,0.0000,0.0000,0.0400 |
| OA(80; 3; 26) | 3494 (3432) | 1.0000 | 1.0000 | all arrays (binary) | 1.0000,0.0000,0.0000,0.0000,0.0000,0.2400,0.0400 |
Strength 3, 88 runs
Maximal number of factors from rank constraints: 12.
| Case | Isomorphisms (full rank) | Best D-efficiency | Best average VIF | Data | Best GWLP |
| OA(88; 3; 24) | 6 (5) | 0.9977 | 1.0045 | all arrays | 1.0000,0.0000,0.0000,0.0000,0.0083 |
| OA(88; 3; 25) | 28 (28) | 0.9921 | 1.0161 | all arrays | 1.0000,0.0000,0.0000,0.0000,0.0413,0.0000 |
| OA(88; 3; 26) | 11041 (10980) | 0.9832 | 1.0351 | all arrays (binary) | 1.0000,0.0000,0.0000,0.0000,0.1240,0.0000,0.0000 |
Strength 3, 96 runs
Maximal number of factors from rank constraints: 13.
| Case | Isomorphisms (full rank) | Best D-efficiency | Best average VIF | Data | Best GWLP |
| OA(96; 3; 24) | 7 (6) | 1.0000 | 1.0000 | all arrays | 1.0000,0.0000,0.0000,0.0000,0.0000 |
| OA(96; 3; 25) | 56 (55) | 1.0000 | 1.0000 | all arrays | 1.0000,0.0000,0.0000,0.0000,0.0000,0.0000 |