Abstract
The traditional approach to designing a screening experiment is to start with a regular fractional factorial design (FFD) of resolution III or IV or a subset of columns of a Plackett–Burman design. This experiment is then followed by the foldover of the design in the initial stage or follow-up runs. This paper introduces a class of 2-level orthogonal minimally aliased designs (OMADs) for screening experiments. These OMADs are constructed by selecting subsets of columns of the Hadamard matrices with two circulant cores using a relaxed version of the minimum G-aberration criterion (Deng & Tang in Commun Stat- Theory Methods 29:1379-1395, 1999). Unlike the regular FFDs of resolutions III and IV, nearly all of our OMADs do not have fully aliased effects. As such, follow-up runs used to disentangle these effects from one another become unnecessary. Our OMADs can also be easily divided into two blocks. The OMADs are compared with the designs of Schoen & Mee (J Royal Stat Soc Ser 61:163-174, 2012), Schoen et al. (J Am Stat Assoc 112:1354-1369, 2017) and regular FFDs. A catalog of 252 OMADs with 16, 20, 24, 28, 32, 36, 40, 44 and 48 runs is then given.
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Appendix: OMADs with 16, 20, 24, 28, 32, 36, 40, 44 and 48 runs
Appendix: OMADs with 16, 20, 24, 28, 32, 36, 40, 44 and 48 runs
\(\#\) | \(n\) | \(m\) | A\(_3\) | A\(_4\) | M\(_3\) | M\(_4\) | df(2FI) | \(r_{\textrm{worst}}\) | PIC\(_5\) |
|---|---|---|---|---|---|---|---|---|---|
1 | 16 | 4 | 0 | 0 | 0 | 0 | 6 | 0 | – |
2 | 16 | 5 | 0 | 0 | 0 | 0 | 10 | 0 | 1 |
3 | 16 | 6 | 1 | 1 | 8 (4) | 8 (4) | 14 | 0.5 | 0.1667 |
4 | 16 | 7 | 2 | 3 | 8 (8) | 8 (12) | 14 | 0.5 | 0.1945 |
5† | 16 | 8 | 3.5 | 7 | 8 (14) | 8 (28) | 14 | 0.5 | 0.1928 |
6 | 16 | 9 | 4 | 14 | 8 (16) | 16 (14) | 15 | 1 | 0.4406 |
7 | 16 | 10 | 8 | 18 | 8 (32) | 16 (10) | 15 | 1 | 0.257 |
8 | 16 | 11 | 12 | 26 | 8 (48) | 16 (10) | 15 | 1 | 0.2203 |
9 | 16 | 12 | 16 | 39 | 8 (64) | 16 (15) | 15 | 1 | 0.2203 |
10 | 16 | 13 | 22 | 55 | 8 (88) | 16 (15) | 15 | 1 | 0.1927 |
11† | 16 | 14 | 28 | 77 | 8 (112) | 16 (21) | 15 | 1 | 0.1927 |
12† | 16 | 15 | 35 | 105 | 16 (7) | 16 (21) | 15 | 1 | 0.1869 |
13 | 20 | 4 | 0.16 | 0.04 | 4 (4) | 4 (1) | 6 | 0.2 | – |
14 | 20 | 5 | 0.4 | 0.2 | 4 (10) | 4 (5) | 10 | 0.2 | 0.866 |
15 | 20 | 6 | 0.8 | 0.6 | 4 (20) | 4 (15) | 15 | 0.2 | 0.8613 |
16 | 20 | 7 | 1.4 | 2.04 | 4 (35) | 12 (2) | 19 | 0.6 | 0.7582 |
17 | 20 | 8 | 2.24 | 4.72 | 4 (56) | 12 (6) | 19 | 0.6 | 0.7599 |
18 | 20 | 9 | 3.36 | 10.8 | 4 (84) | 12 (18) | 18 | 0.6 | 0.6745 |
19 | 20 | 10 | 4.8 | 18 | 4 (120) | 12 (30) | 19 | 0.6 | 0.6744 |
20 | 20 | 11 | 8.2 | 22.8 | 12 (5) | 12 (30) | 19 | 0.6 | 0.6687 |
21 | 20 | 12 | 11.36 | 32.28 | 12 (8) | 12 (39) | 19 | 0.6 | 0.6392 |
22 | 20 | 13 | 15.92 | 43.64 | 12 (14) | 12 (47) | 19 | 0.6 | 0.6002 |
23 | 20 | 14 | 20.96 | 59.24 | 12 (20) | 12 (60) | 19 | 0.6 | 0.5527 |
24 | 20 | 15 | 26.52 | 80.52 | 12 (26) | 12 (81) | 19 | 0.6 | 0.545 |
25 | 20 | 16 | 32.64 | 107.36 | 12 (32) | 12 (108) | 19 | 0.6 | 0.5441 |
26 | 20 | 17 | 40 | 140 | 12 (40) | 12 (140) | 19 | 0.6 | 0.5385 |
27† | 20 | 18 | 48 | 180 | 12 (48) | 12 (180) | 19 | 0.6 | 0.5385 |
28† | 20 | 19 | 57 | 228 | 12 (57) | 12 (228) | 19 | 0.6 | 0.5385 |
29 | 24 | 4 | 0 | 0.11 | 0 | 8 (1) | 6 | 0.333 | – |
30 | 24 | 5 | 0 | 0.56 | 0 | 8 (5) | 10 | 0.333 | 0.868 |
31 | 24 | 6 | 0 | 1.67 | 0 | 8 (15) | 11 | 0.333 | 0.868 |
32 | 24 | 7 | 0 | 3.89 | 0 | 8 (35) | 11 | 0.333 | 0.868 |
33 | 24 | 8 | 0 | 7.78 | 0 | 8 (70) | 11 | 0.333 | 0.868 |
34 | 24 | 9 | 0 | 14 | 0 | 8 (126) | 11 | 0.333 | 0.868 |
35 | 24 | 10 | 0 | 23.33 | 0 | 8 (210) | 11 | 0.333 | 0.868 |
36 | 24 | 11 | 0 | 36.67 | 0 | 8 (330) | 11 | 0.333 | 0.868 |
37 | 24 | 12 | 0 | 55 | 0 | 8 (495) | 11 | 0.333 | 0.868 |
38 | 24 | 13 | 12.67 | 34.78 | 8 (114) | 8 (313) | 23 | 0.333 | 0.7822 |
39 | 24 | 14 | 16.56 | 48 | 8 (149) | 8 (432) | 23 | 0.333 | 0.7764 |
40 | 24 | 15 | 21 | 65.44 | 8 (189) | 8 (589) | 23 | 0.333 | 0.7677 |
\(\#\) | \(n\) | \(m\) | A\(_3\) | A\(_4\) | M\(_3\) | M\(_4\) | df(2FI) | \(r_{\textrm{worst}}\) | PIC\(_5\) |
|---|---|---|---|---|---|---|---|---|---|
41 | 24 | 16 | 26.11 | 87 | 8 (235) | 8 (783) | 23 | 0.333 | 0.762 |
42 | 24 | 17 | 31.89 | 113.78 | 8 (287) | 8 (1024) | 23 | 0.333 | 0.7583 |
43 | 24 | 18 | 38.56 | 145.89 | 8 (347) | 8 (1313) | 23 | 0.333 | 0.7555 |
44 | 24 | 19 | 46 | 184.67 | 8 (414) | 8 (1662) | 23 | 0.333 | 0.7547 |
45 | 24 | 20 | 54.22 | 230.78 | 8 (488) | 8 (2077) | 23 | 0.333 | 0.7533 |
46 | 24 | 21 | 63.33 | 285 | 8 (570) | 8 (2565) | 23 | 0.333 | 0.7525 |
47† | 24 | 22 | 73.33 | 348.33 | 8 (660) | 8 (3135) | 23 | 0.333 | 0.7525 |
48† | 24 | 23 | 84.33 | 421.67 | 8 (759) | 8 (3795) | 23 | 0.333 | 0.7525 |
49 | 28 | 4 | 0.08 | 0.02 | 4 (4) | 4 (1) | 6 | 0.143 | – |
50 | 28 | 5 | 0.2 | 0.1 | 4 (10) | 4 (5) | 10 | 0.143 | 0.935 |
51 | 28 | 6 | 0.41 | 0.31 | 4 (20) | 4 (15) | 15 | 0.143 | 0.9367 |
52 | 28 | 7 | 0.71 | 0.88 | 4 (35) | 12 (1) | 21 | 0.429 | 0.9307 |
53 | 28 | 8 | 1.14 | 2.9 | 4 (56) | 12 (9) | 27 | 0.429 | 0.9099 |
54 | 28 | 9 | 1.71 | 5.51 | 4 (84) | 12 (18) | 27 | 0.429 | 0.907 |
55 | 28 | 10 | 2.45 | 13.59 | 4 (120) | 12 (57) | 23 | 0.429 | 0.8794 |
56 | 28 | 11 | 3.37 | 21.43 | 4 (165) | 12 (90) | 24 | 0.429 | 0.8791 |
57 | 28 | 12 | 4.49 | 32.14 | 4 (220) | 12 (135) | 25 | 0.429 | 0.8791 |
58† | 28 | 13 | 5.84 | 46.43 | 4 (286) | 12 (195) | 26 | 0.429 | 0.8791 |
59† | 28 | 14 | 7.43 | 65 | 4 (364) | 12 (273) | 27 | 0.429 | 0.8793 |
60 | 28 | 15 | 15.98 | 57.41 | 12 (41) | 12 (181) | 27 | 0.429 | 0.8708 |
61 | 28 | 16 | 20.73 | 74.69 | 12 (57) | 12 (230) | 27 | 0.429 | 0.8664 |
62 | 28 | 17 | 25.96 | 96.24 | 12 (74) | 12 (292) | 27 | 0.429 | 0.8636 |
63 | 28 | 18 | 31.35 | 124.16 | 12 (90) | 12 (378) | 27 | 0.429 | 0.8627 |
64 | 28 | 19 | 37.9 | 156 | 12 (111) | 12 (471) | 27 | 0.429 | 0.8611 |
65 | 28 | 20 | 44.82 | 195.04 | 12 (132) | 12 (589) | 27 | 0.429 | 0.8604 |
66 | 28 | 21 | 52.61 | 240.18 | 12 (156) | 12 (723) | 27 | 0.429 | 0.8599 |
67 | 28 | 22 | 61.31 | 292.8 | 12 (183) | 12 (879) | 27 | 0.429 | 0.8593 |
68 | 28 | 23 | 70.59 | 354.43 | 12 (211) | 12 (1064) | 27 | 0.429 | 0.8591 |
69 | 28 | 24 | 80.82 | 425.18 | 12 (242) | 12 (1276) | 27 | 0.429 | 0.8589 |
70 | 28 | 25 | 92 | 506 | 12 (276) | 12 (1518) | 27 | 0.429 | 0.8587 |
71† | 28 | 26 | 104 | 598 | 12 (312) | 12 (1794) | 27 | 0.429 | 0.8587 |
72† | 28 | 27 | 117 | 702 | 12 (351) | 12 (2106) | 27 | 0.429 | 0.8587 |
73 | 32 | 4 | 0 | 0 | 0 | 0 | 6 | 0 | – |
74 | 32 | 5 | 0 | 0 | 0 | 0 | 10 | 0 | 1 |
75 | 32 | 6 | 0 | 0 | 0 | 0 | 15 | 0 | 1 |
76 | 32 | 7 | 0.31 | 0.88 | 8 (5) | 8 (14) | 21 | 0.25 | 0.9556 |
77 | 32 | 8 | 0.75 | 2.5 | 8 (12) | 8 (40) | 28 | 0.25 | 0.9336 |
78 | 32 | 9 | 1.81 | 4.88 | 8 (30) | 8 (78) | 29 | 0.25 | 0.9097 |
79 | 32 | 10 | 3.44 | 6.81 | 8 (55) | 8 (109) | 31 | 0.25 | 0.9031 |
80 | 32 | 11 | 4.88 | 11.5 | 8 (78) | 8 (184) | 31 | 0.25 | 0.8978 |
81 | 32 | 12 | 6.69 | 17.31 | 8 (107) | 8 (277) | 31 | 0.25 | 0.8955 |
82 | 32 | 13 | 8.94 | 24.88 | 8 (143) | 8 (398) | 31 | 0.25 | 0.8936 |
83 | 32 | 14 | 11.62 | 34.38 | 8 (186) | 8 (550) | 31 | 0.25 | 0.8925 |
84 | 32 | 15 | 14.75 | 47.88 | 8 (236) | 8 (766) | 31 | 0.25 | 0.8902 |
85 | 32 | 16 | 18.38 | 63.12 | 8 (294) | 8 (1010) | 31 | 0.25 | 0.8897 |
86 | 32 | 17 | 22.5 | 82.12 | 8 (360) | 8 (1314) | 31 | 0.25 | 0.8892 |
87 | 32 | 18 | 27.25 | 105.38 | 8 (436) | 8 (1686) | 31 | 0.25 | 0.8885 |
88 | 32 | 19 | 32.56 | 133.38 | 8 (521) | 8 (2134) | 31 | 0.25 | 0.888 |
89 | 32 | 20 | 38.44 | 167.44 | 8 (615) | 8 (2679) | 31 | 0.25 | 0.8875 |
90 | 32 | 21 | 45 | 206.62 | 8 (720) | 8 (3306) | 31 | 0.25 | 0.8872 |
91 | 32 | 22 | 52.31 | 252.56 | 8 (837) | 8 (4041) | 31 | 0.25 | 0.8869 |
92 | 32 | 23 | 60.38 | 305.88 | 8 (966) | 8 (4894) | 31 | 0.25 | 0.8865 |
93 | 32 | 24 | 69.25 | 366.88 | 8 (1108) | 8 (5870) | 31 | 0.25 | 0.8862 |
94 | 32 | 25 | 78.94 | 436.5 | 8 (1263) | 8 (6984) | 31 | 0.25 | 0.886 |
\(\#\) | \(n\) | \(m\) | A\(_3\) | A\(_4\) | M\(_3\) | M\(_4\) | df(2FI) | \(r_{\textrm{worst}}\) | PIC\(_5\) |
|---|---|---|---|---|---|---|---|---|---|
95 | 32 | 26 | 89.38 | 515.62 | 8 (1430) | 8 (8250) | 31 | 0.25 | 0.8858 |
96 | 32 | 27 | 100.75 | 605.25 | 8 (1612) | 8 (9684) | 31 | 0.25 | 0.8856 |
97 | 32 | 28 | 112.94 | 706.06 | 8 (1807) | 8 (11297) | 31 | 0.25 | 0.8856 |
98 | 32 | 29 | 126 | 819 | 8 (2016) | 8 (13104) | 31 | 0.25 | 0.8856 |
99† | 32 | 30 | 140 | 945 | 8 (2240) | 8 (15120) | 31 | 0.25 | 0.8856 |
100† | 32 | 31 | 155 | 1085 | 8 (2480) | 8 (17360) | 31 | 0.25 | 0.8856 |
101 | 36 | 4 | 0.05 | 0.01 | 4 (4) | 4 (1) | 6 | 0.111 | – |
102 | 36 | 5 | 0.12 | 0.06 | 4 (10) | 4 (5) | 10 | 0.111 | 0.963 |
103 | 36 | 6 | 0.25 | 0.19 | 4 (20) | 4 (15) | 15 | 0.111 | 0.9635 |
104 | 36 | 7 | 0.43 | 0.43 | 4 (35) | 4 (35) | 21 | 0.111 | 0.964 |
105 | 36 | 8 | 0.69 | 1.75 | 4 (56) | 12 (9) | 28 | 0.333 | 0.9489 |
106 | 36 | 9 | 1.04 | 3.83 | 4 (84) | 12 (23) | 35 | 0.333 | 0.9428 |
107 | 36 | 10 | 1.48 | 10.4 | 4 (120) | 12 (79) | 27 | 0.333 | 0.92 |
108 | 36 | 11 | 2.04 | 16.72 | 4 (165) | 12 (128) | 28 | 0.333 | 0.9187 |
109 | 36 | 12 | 2.72 | 25.07 | 4 (220) | 12 (192) | 29 | 0.333 | 0.9186 |
110 | 36 | 13 | 3.53 | 36.88 | 4 (286) | 12 (284) | 30 | 0.333 | 0.9176 |
111 | 36 | 14 | 4.49 | 51.86 | 4 (364) | 12 (400) | 31 | 0.333 | 0.9173 |
112 | 36 | 15 | 5.62 | 70.78 | 4 (455) | 12 (546) | 32 | 0.333 | 0.9173 |
113 | 36 | 16 | 6.91 | 94.37 | 4 (560) | 12 (728) | 33 | 0.333 | 0.9173 |
114† | 36 | 17 | 8.4 | 123.41 | 4 (680) | 12 (952) | 34 | 0.333 | 0.9173 |
115† | 36 | 18 | 10.07 | 158.67 | 4 (816) | 12 (1224) | 35 | 0.333 | 0.9172 |
116 | 36 | 19 | 27.77 | 120.25 | 12 (160) | 12 (733) | 35 | 0.333 | 0.9049 |
117 | 36 | 20 | 32.94 | 148.9 | 12 (191) | 12 (902) | 35 | 0.333 | 0.9046 |
118 | 36 | 21 | 38.74 | 182.63 | 12 (226) | 12 (1101) | 35 | 0.333 | 0.9043 |
119 | 36 | 22 | 45.19 | 224.04 | 12 (265) | 12 (1354) | 35 | 0.333 | 0.9037 |
120 | 36 | 23 | 51.99 | 271.79 | 12 (305) | 12 (1645) | 35 | 0.333 | 0.9036 |
121 | 36 | 24 | 59.95 | 323.28 | 12 (354) | 12 (1945) | 35 | 0.333 | 0.9032 |
122 | 36 | 25 | 68.4 | 385.01 | 12 (405) | 12 (2317) | 36 | 0.333 | 0.9028 |
123 | 36 | 26 | 77.53 | 455.09 | 12 (460) | 12 (2739) | 35 | 0.333 | 0.9026 |
124 | 36 | 27 | 87.47 | 533.8 | 12 (520) | 12 (3211) | 35 | 0.333 | 0.9024 |
125 | 36 | 28 | 98.12 | 622.46 | 12 (584) | 12 (3743) | 35 | 0.333 | 0.9023 |
126 | 36 | 29 | 109.8 | 721.17 | 12 (655) | 12 (4333) | 35 | 0.333 | 0.9021 |
127 | 36 | 30 | 122.22 | 831.67 | 12 (730) | 12 (4995) | 35 | 0.333 | 0.902 |
128 | 36 | 31 | 135.89 | 953.89 | 12 (814) | 12 (5725) | 35 | 0.333 | 0.9017 |
129 | 36 | 32 | 150.22 | 1089.78 | 12 (901) | 12 (6539) | 35 | 0.333 | 0.9016 |
130 | 36 | 33 | 165.33 | 1240 | 12 (992) | 12 (7440) | 35 | 0.333 | 0.9015 |
131† | 36 | 34 | 181.33 | 1405.33 | 12 (1088) | 12 (8432) | 35 | 0.333 | 0.9015 |
132† | 36 | 35 | 198.33 | 1586.67 | 12 (1190) | 12 (9520) | 35 | 0.333 | 0.9015 |
133 | 40 | 4 | 0 | 0.04 | 0 (4) | 8 (1) | 6 | 0.2 | – |
134 | 40 | 5 | 0 | 0.2 | 0 (10) | 8 (5) | 10 | 0.2 | 0.958 |
135 | 40 | 6 | 0 | 0.6 | 0 (20) | 8 (15) | 15 | 0.2 | 0.958 |
136 | 40 | 7 | 0 | 1.4 | 0 (35) | 8 (35) | 21 | 0.2 | 0.9583 |
137 | 40 | 8 | 0 | 2.8 | 0 (56) | 8 (70) | 25 | 0.2 | 0.9583 |
138 | 40 | 9 | 0 | 5.04 | 0 (84) | 8 (126) | 27 | 0.2 | 0.9583 |
139 | 40 | 10 | 0 | 8.4 | 0 (120) | 8 (210) | 27 | 0.2 | 0.9583 |
140 | 40 | 11 | 1.8 | 15.2 | 8 (45) | 16 (37) | 29 | 0.4 | 0.9276 |
141 | 40 | 12 | 2.48 | 23 | 8 (62) | 16 (56) | 30 | 0.4 | 0.9263 |
142 | 40 | 13 | 3.28 | 33.4 | 8 (82) | 16 (82) | 31 | 0.4 | 0.9256 |
143 | 40 | 14 | 4.2 | 47.12 | 8 (105) | 16 (118) | 32 | 0.4 | 0.925 |
144 | 40 | 15 | 5.32 | 64.12 | 8 (133) | 16 (160) | 33 | 0.4 | 0.9248 |
145 | 40 | 16 | 6.56 | 85.6 | 8 (164) | 16 (214) | 34 | 0.4 | 0.9247 |
146 | 40 | 17 | 8 | 112 | 8 (200) | 16 (280) | 35 | 0.4 | 0.9246 |
\(\#\) | \(n\) | \(m\) | A\(_3\) | A\(_4\) | M\(_3\) | M\(_4\) | df(2FI) | \(r_{\textrm{worst}}\) | PIC\(_5\) |
|---|---|---|---|---|---|---|---|---|---|
147 | 40 | 18 | 9.6 | 144 | 8 (240) | 16 (360) | 36 | 0.4 | 0.9246 |
148† | 40 | 19 | 11.4 | 182.4 | 8 (285) | 16 (456) | 37 | 0.4 | 0.9246 |
149† | 40 | 20 | 11.4 | 228 | 8 (285) | 16 (570) | 38 | 0.4 | 0.9283 |
150 | 40 | 21 | 35.32 | 161.96 | 16 (38) | 24 (14) | 39 | 0.6 | 0.9145 |
151 | 40 | 22 | 40.8 | 198.2 | 16 (43) | 24 (17) | 39 | 0.6 | 0.9147 |
152 | 40 | 23 | 47.16 | 239.08 | 16 (54) | 24 (20) | 39 | 0.6 | 0.9144 |
153 | 40 | 24 | 53.76 | 288.64 | 16 (62) | 24 (24) | 39 | 0.6 | 0.9144 |
154 | 40 | 25 | 61.92 | 342.48 | 16 (72) | 24 (31) | 39 | 0.6 | 0.9136 |
155 | 40 | 26 | 70.36 | 404.04 | 16 (84) | 24 (33) | 39 | 0.6 | 0.9133 |
156 | 40 | 27 | 79.16 | 474.72 | 16 (97) | 24 (40) | 39 | 0.6 | 0.9133 |
157 | 40 | 28 | 88.08 | 553.72 | 16 (109) | 24 (49) | 39 | 0.6 | 0.9137 |
158 | 40 | 29 | 98.72 | 641.32 | 16 (121) | 24 (53) | 39 | 0.6 | 0.9135 |
159 | 40 | 30 | 109.92 | 740.52 | 16 (139) | 24 (63) | 39 | 0.6 | 0.9133 |
160 | 40 | 31 | 121.24 | 850.52 | 16 (154) | 24 (72) | 39 | 0.6 | 0.9135 |
161 | 40 | 32 | 134 | 971.68 | 16 (173) | 24 (82) | 39 | 0.6 | 0.9134 |
162 | 40 | 33 | 147.36 | 1105.92 | 16 (194) | 24 (93) | 39 | 0.6 | 0.9134 |
163 | 40 | 34 | 161.64 | 1253.48 | 16 (216) | 24 (107) | 39 | 0.6 | 0.9134 |
164 | 40 | 35 | 176.92 | 1415.12 | 16 (240) | 24 (123) | 39 | 0.6 | 0.9134 |
165 | 40 | 36 | 192.96 | 1592.04 | 16 (266) | 24 (137) | 39 | 0.6 | 0.9134 |
166 | 40 | 37 | 210 | 1785 | 16 (294) | 24 (153) | 39 | 0.6 | 0.9133 |
167† | 40 | 38 | 228 | 1995 | 16 (323) | 24 (171) | 39 | 0.6 | 0.9133 |
168† | 40 | 39 | 247 | 2223 | 16 (361) | 24 (171) | 39 | 0.6 | 0.9133 |
169 | 44 | 4 | 0.03 | 0.01 | 4 (4) | 4 (1) | 6 | 0.091 | – |
170 | 44 | 5 | 0.08 | 0.04 | 4 (10) | 4 (5) | 10 | 0.091 | 0.976 |
171 | 44 | 6 | 0.17 | 0.12 | 4 (20) | 4 (15) | 15 | 0.091 | 0.9763 |
172 | 44 | 7 | 0.29 | 0.29 | 4 (35) | 4 (35) | 21 | 0.091 | 0.9762 |
173 | 44 | 8 | 0.46 | 1.04 | 4 (56) | 12 (7) | 28 | 0.273 | 0.9691 |
174 | 44 | 9 | 0.69 | 2.63 | 4 (84) | 12 (24) | 36 | 0.273 | 0.9625 |
175 | 44 | 10 | 0.99 | 6.17 | 4 (120) | 12 (67) | 42 | 0.273 | 0.9531 |
176 | 44 | 11 | 1.63 | 9.93 | 12 (4) | 12 (109) | 43 | 0.273 | 0.9488 |
177 | 44 | 12 | 4.2 | 12.16 | 12 (36) | 12 (122) | 43 | 0.273 | 0.935 |
178 | 44 | 13 | 5.67 | 18.6 | 12 (50) | 12 (192) | 43 | 0.273 | 0.9316 |
179 | 44 | 14 | 7.5 | 25.33 | 12 (68) | 12 (258) | 43 | 0.273 | 0.9307 |
180 | 44 | 15 | 9.58 | 34.36 | 12 (88) | 12 (349) | 43 | 0.273 | 0.9298 |
181 | 44 | 16 | 12.1 | 45.59 | 12 (113) | 12 (462) | 43 | 0.273 | 0.9288 |
182 | 44 | 17 | 15.01 | 59.6 | 12 (142) | 12 (604) | 43 | 0.273 | 0.9277 |
183 | 44 | 18 | 18.38 | 73.95 | 12 (176) | 12 (736) | 43 | 0.273 | 0.9277 |
184 | 44 | 19 | 22.29 | 96.36 | 12 (216) | 12 (973) | 43 | 0.273 | 0.9259 |
185 | 44 | 20 | 26.21 | 119.31 | 12 (254) | 12 (1199) | 43 | 0.273 | 0.9262 |
186 | 44 | 21 | 30.83 | 149.23 | 12 (300) | 12 (1509) | 43 | 0.273 | 0.9254 |
187 | 44 | 22 | 36.07 | 180.19 | 12 (353) | 12 (1811) | 43 | 0.273 | 0.9252 |
188 | 44 | 23 | 41.61 | 216.59 | 12 (408) | 12 (2169) | 43 | 0.273 | 0.9252 |
189 | 44 | 24 | 47.8 | 261.04 | 12 (470) | 12 (2620) | 43 | 0.273 | 0.9249 |
190 | 44 | 25 | 54.71 | 309.37 | 12 (540) | 12 (3098) | 43 | 0.273 | 0.9246 |
191 | 44 | 26 | 62.08 | 366.07 | 12 (614) | 12 (3668) | 43 | 0.273 | 0.9244 |
192 | 44 | 27 | 69.86 | 430.66 | 12 (691) | 12 (4320) | 43 | 0.273 | 0.9243 |
193 | 44 | 28 | 78.71 | 500.26 | 12 (781) | 12 (5007) | 43 | 0.273 | 0.9241 |
194 | 44 | 29 | 87.92 | 580.75 | 12 (873) | 12 (5815) | 43 | 0.273 | 0.924 |
195 | 44 | 30 | 97.95 | 669.07 | 12 (974) | 12 (6694) | 43 | 0.273 | 0.9239 |
196 | 44 | 31 | 108.55 | 768.47 | 12 (1080) | 12 (7690) | 43 | 0.273 | 0.9238 |
197 | 44 | 32 | 120.07 | 878.02 | 12 (1196) | 12 (8785) | 43 | 0.273 | 0.9237 |
198 | 44 | 33 | 132.3 | 999.27 | 12 (1319) | 12 (9999) | 43 | 0.273 | 0.9236 |
199 | 44 | 34 | 145.26 | 1131.83 | 12 (1449) | 12 (11322) | 43 | 0.273 | 0.9236 |
200 | 44 | 35 | 159.02 | 1277.69 | 12 (1587) | 12 (12780) | 43 | 0.273 | 0.9235 |
\(\#\) | \(n\) | \(m\) | A\(_3\) | A\(_4\) | M\(_3\) | M\(_4\) | df(2FI) | \(r_{\textrm{worst}}\) | PIC\(_5\) |
|---|---|---|---|---|---|---|---|---|---|
201 | 44 | 36 | 173.65 | 1437.17 | 12 (1734) | 12 (14374) | 43 | 0.273 | 0.9235 |
202 | 44 | 37 | 189.11 | 1611.35 | 12 (1889) | 12 (16116) | 43 | 0.273 | 0.9234 |
203 | 44 | 38 | 205.52 | 1800.52 | 12 (2054) | 12 (18006) | 43 | 0.273 | 0.9234 |
204 | 44 | 39 | 222.77 | 2006.24 | 12 (2227) | 12 (20063) | 43 | 0.273 | 0.9233 |
205 | 44 | 40 | 240.93 | 2229.07 | 12 (2409) | 12 (22291) | 43 | 0.273 | 0.9233 |
206 | 44 | 41 | 260 | 2470 | 12 (2600) | 12 (24700) | 43 | 0.273 | 0.9233 |
207† | 44 | 42 | 280 | 2730 | 12 (2800) | 12 (27300) | 43 | 0.273 | 0.9233 |
208† | 44 | 43 | 301 | 3010 | 12 (3010) | 12 (30100) | 43 | 0.273 | 0.9233 |
209 | 48 | 4 | 0 | 0 | 0 | 0 | 6 | 0 | – |
210 | 48 | 5 | 0 | 0 | 0 | 0 | 10 | 0 | 1 |
211 | 48 | 6 | 0 | 0.11 | 0 | 16 (1) | 15 | 0.333 | 0.9927 |
212 | 48 | 7 | 0 | 0.33 | 0 | 16 (3) | 21 | 0.333 | 0.9906 |
213 | 48 | 8 | 0 | 1.22 | 0 | 16 (11) | 27 | 0.333 | 0.9819 |
214 | 48 | 9 | 0 | 2.44 | 0 | 16 (22) | 29 | 0.333 | 0.9798 |
215 | 48 | 10 | 0 | 5.33 | 0 | 16 (48) | 31 | 0.333 | 0.973 |
216 | 48 | 11 | 0 | 9.11 | 0 | 16 (82) | 32 | 0.333 | 0.9706 |
217 | 48 | 12 | 0 | 15.33 | 0 | 16 (138) | 33 | 0.333 | 0.9668 |
218 | 48 | 13 | 0 | 23 | 0 | 16 (207) | 34 | 0.333 | 0.9655 |
219 | 48 | 14 | 2.72 | 40.06 | 8 (98) | 16 (289) | 36 | 0.333 | 0.9422 |
220 | 48 | 15 | 3.5 | 53.72 | 8 (126) | 16 (385) | 37 | 0.333 | 0.9425 |
221 | 48 | 16 | 4.33 | 71.94 | 8 (156) | 16 (517) | 38 | 0.333 | 0.9422 |
222 | 48 | 17 | 5.33 | 94.06 | 8 (192) | 16 (676) | 39 | 0.333 | 0.942 |
223 | 48 | 18 | 6.42 | 121.31 | 8 (231) | 16 (873) | 40 | 0.333 | 0.9418 |
224 | 48 | 19 | 7.67 | 153.67 | 8 (276) | 16 (1106) | 41 | 0.333 | 0.9417 |
225 | 48 | 20 | 9.03 | 192.25 | 8 (325) | 16 (1384) | 42 | 0.333 | 0.9417 |
226 | 48 | 21 | 10.56 | 237.5 | 8 (380) | 16 (1710) | 43 | 0.333 | 0.9416 |
227 | 48 | 22 | 12.22 | 290.28 | 8 (440) | 16 (2090) | 44 | 0.333 | 0.9416 |
228† | 48 | 23 | 14.06 | 351.39 | 8 (506) | 16 (2530) | 45 | 0.333 | 0.9416 |
229† | 48 | 24 | 14.06 | 421.67 | 8 (506) | 16 (3036) | 46 | 0.333 | 0.9437 |
230 | 48 | 25 | 49.39 | 281.67 | 16 (135) | 16 (852) | 47 | 0.333 | 0.9323 |
231 | 48 | 26 | 56.22 | 334.61 | 16 (156) | 16 (1016) | 47 | 0.333 | 0.9319 |
232 | 48 | 27 | 63.22 | 393.5 | 16 (176) | 16 (1201) | 47 | 0.333 | 0.9318 |
233 | 48 | 28 | 70.78 | 457.56 | 16 (197) | 16 (1387) | 47 | 0.333 | 0.9319 |
234 | 48 | 29 | 79.44 | 530.39 | 16 (227) | 16 (1600) | 47 | 0.333 | 0.9316 |
235 | 48 | 30 | 88.42 | 612.36 | 16 (255) | 16 (1852) | 47 | 0.333 | 0.9316 |
236 | 48 | 31 | 98.5 | 700.78 | 16 (285) | 16 (2108) | 47 | 0.333 | 0.9313 |
237 | 48 | 32 | 109.03 | 800.58 | 16 (317) | 16 (2412) | 47 | 0.333 | 0.9312 |
238 | 48 | 33 | 119.83 | 911.33 | 16 (350) | 16 (2743) | 47 | 0.333 | 0.9312 |
239 | 48 | 34 | 131.58 | 1032.08 | 16 (386) | 16 (3104) | 47 | 0.333 | 0.9312 |
240 | 48 | 35 | 144.44 | 1164.44 | 16 (425) | 16 (3499) | 47 | 0.333 | 0.931 |
241 | 48 | 36 | 157.64 | 1310.08 | 16 (465) | 16 (3938) | 47 | 0.333 | 0.931 |
242 | 48 | 37 | 171.81 | 1468.56 | 16 (509) | 16 (4413) | 47 | 0.333 | 0.9309 |
243 | 48 | 38 | 186.72 | 1641 | 16 (554) | 16 (4929) | 47 | 0.333 | 0.9309 |
244 | 48 | 39 | 202.08 | 1828.94 | 16 (602) | 16 (5490) | 47 | 0.333 | 0.9309 |
245 | 48 | 40 | 219.06 | 2031.28 | 16 (653) | 16 (6098) | 47 | 0.333 | 0.9308 |
246 | 48 | 41 | 236.47 | 2250.94 | 16 (706) | 16 (6757) | 47 | 0.333 | 0.9308 |
247 | 48 | 42 | 254.78 | 2487.83 | 16 (762) | 16 (7467) | 47 | 0.333 | 0.9307 |
248 | 48 | 43 | 274.06 | 2742.61 | 16 (821) | 16 (8229) | 47 | 0.333 | 0.9307 |
249 | 48 | 44 | 294.22 | 3016.78 | 16 (882) | 16 (9051) | 47 | 0.333 | 0.9307 |
250 | 48 | 45 | 315.33 | 3311 | 16 (946) | 16 (9933) | 47 | 0.333 | 0.9307 |
251† | 48 | 46 | 337.33 | 3626.33 | 16 (1012) | 16 (10879) | 47 | 0.333 | 0.9307 |
252† | 48 | 47 | 360.33 | 3963.67 | 16 (1081) | 16 (11891) | 47 | 0.333 | 0.9307 |
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Nguyen, NK., Pham, TD. & Vuong, M.P. A Catalog of 2-Level Orthogonal Minimally Aliased Designs with Small Runs. J Stat Theory Pract 17, 26 (2023). https://doi.org/10.1007/s42519-023-00321-y
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DOI: https://doi.org/10.1007/s42519-023-00321-y