Further examples

Calculations of PFTs and ICFTs have been done with R package DoE.base (Grömping 2016), while MAFTs have been calculated with separate R functions.

Metrics for the 5-level Latin squares of Fontana et al. (2016)

Table 1: The 5-level Latin squares of Fontana et al. (2016), swapped MAFT has levels 1 and 2 of last column swapped
0 1/50 1/25 3/50 2/25 1/10 3/25 1/5 11/50 3/10 9/25 1 4
d1 ICFTc 63 0 0 0 0 0 0 0 0 0 0 0 1
ICFTe 63 0 0 0 0 0 0 0 0 0 0 0 1
MAFTorig. 12 0 16 32 0 0 0 0 0 0 4 0 0
MAFTswapped 0 24 12 4 8 8 4 0 4 0 0 0 0
d2 ICFTc 63 0 0 0 0 0 0 0 0 0 0 0 1
ICFTe 63 0 0 0 0 0 0 0 0 0 0 0 1
MAFTorig. 60 0 0 0 0 0 0 0 0 0 0 4 0
MAFTswapped 48 0 0 0 0 0 0 8 0 8 0 0 0

The 24 non-isomorphic 36 run 33 designs

These designs were obtained from Pieter Eendebak, who created them with the method published in Schoen, Eendebak and Nguyen (2010).

Table 2: Metrics for non-isomorphic 36 run 33 designs, designs 1 and 2.
0 1 2
a3 0 0 1
ICFTc 7 0 1
ICFTe 7 0 1
MAFT 6 2 0
0 1/16 1/8 9/16 9/8 5/4
a3 0 0 0 0 0 1
ICFTc 6 0 1 0 1 0
ICFTe 6 0 1 0 1 0
MAFT 4 2 0 2 0 0
Table 2: Metrics for non-isomorphic 36 run 33 designs, designs 3 and 5.
0 1/4 1/2 1
a3 0 0 0 1
ICFTc 7 0 0 1
ICFTe 6 0 2 0
MAFT 4 4 0 0
0 1/48 0.023 1/16 19/48 0.768 11/12
a3 0 0 0 0 0 0 1
ICFTc 4 0 1 2 0 1 0
ICFTe 0 6 1 0 0 1 0
MAFT 0 6 0 0 2 0 0
Table 2: Metrics for non-isomorphic 36 run 33 designs, designs 20 and 4.
0 0.201 7/16 0.674 7/8
a3 0 0 0 0 1
ICFTc 6 1 0 1 0
ICFTe 6 1 0 1 0
MAFT 6 0 2 0 0
0 1/16 1/8 1/4 1/2 3/4
a3 0 0 0 0 0 1
ICFTc 6 0 0 1 1 0
ICFTe 5 0 2 0 1 0
MAFT 2 4 0 2 0 0
Table 2: Metrics for non-isomorphic 36 run 33 designs, designs 12 and 6.
0 1/48 1/16 0.091 13/48 23/51 2/3
a3 0 0 0 0 0 0 1
ICFTc 4 0 2 1 0 1 0
ICFTe 0 6 0 1 0 1 0
MAFT 0 6 0 0 2 0 0
0 1/48 0.023 1/24 0.046 7/48 0.269 0.537 2/3
a3 0 0 0 0 0 0 0 0 1
ICFTc 4 0 0 2 1 0 0 1 0
ICFTe 0 4 2 0 0 0 2 0 0
MAFT 0 4 0 0 0 4 0 0 0
Table 2: Metrics for non-isomorphic 36 run 33 designs, designs 7 and 13.
0 1/12 1/3 2/3
a3 0 0 0 1
ICFTc 6 0 2 0
ICFTe 0 8 0 0
MAFT 0 8 0 0
0 1/16 1/8 1/4 1/2 5/8
a3 0 0 0 0 0 1
ICFTc 6 0 1 0 1 0
ICFTe 6 0 1 0 1 0
MAFT 4 2 0 2 0 0
Table 2: Metrics for non-isomorphic 36 run 33 designs, designs 11 and 9.
0 1/48 0.023 1/24 1/12 7/48 0.269 13/24
a3 0 0 0 0 0 0 0 1
ICFTc 2 0 1 2 2 0 1 0
ICFTe 0 4 1 0 2 0 1 0
MAFT 0 4 0 0 2 2 0 0
0 1/16 1/8 1/2
a3 0 0 0 1
ICFTc 7 0 0 1
ICFTe 4 0 4 0
MAFT 0 8 0 0
Table 2: Metrics for non-isomorphic 36 run 33 designs, designs 16 and 19.
0 1/32 1/16 3/32 1/8 3/8 1/2
a3 0 0 0 0 0 0 1
ICFTc 6 0 0 0 1 1 0
ICFTe 0 4 0 4 0 0 0
MAFT 0 0 8 0 0 0 0
0 1/16 1/8 3/16 1/2
a3 0 0 0 0 1
ICFTc 5 0 1 2 0
ICFTe 5 0 1 2 0
MAFT 4 2 0 2 0
Table 2: Metrics for non-isomorphic 36 run 33 designs, designs 21 and 8.
0 1/4 1/2
a3 0 0 1
ICFTc 7 0 1
ICFTe 7 0 1
MAFT 6 2 0
0 1/16 1/8 1/2
a3 0 0 0 1
ICFTc 7 0 0 1
ICFTe 4 0 4 0
MAFT 0 8 0 0
Table 2: Metrics for non-isomorphic 36 run 33 designs, designs 10 and 14.
0 1/48 0.023 1/16 7/48 0.269 5/12
a3 0 0 0 0 0 0 1
ICFTc 4 0 1 2 0 1 0
ICFTe 0 6 1 0 0 1 0
MAFT 0 6 0 0 2 0 0
0 1/48 1/24 1/12 1/6 5/12
a3 0 0 0 0 0 1
ICFTc 4 0 2 0 2 0
ICFTe 0 4 0 4 0 0
MAFT 0 4 0 4 0 0
Table 2: Metrics for non-isomorphic 36 run 33 designs, designs 18 and 15.
0 1/48 0.023 1/16 7/48 0.269 5/12
a3 0 0 0 0 0 0 1
ICFTc 4 0 1 2 0 1 0
ICFTe 0 6 1 0 0 1 0
MAFT 0 6 0 0 2 0 0
0 1/24 1/16 1/12 1/8 1/4 3/8
a3 0 0 0 0 0 0 1
ICFTc 6 0 0 0 1 1 0
ICFTe 2 3 0 3 0 0 0
MAFT 2 0 6 0 0 0 0
Table 2: Metrics for non-isomorphic 36 run 33 designs, designs 17 and 22.
0 1/48 1/16 1/12 7/24
a3 0 0 0 0 1
ICFTc 4 0 2 2 0
ICFTe 0 6 0 2 0
MAFT 0 6 0 2 0
0 1/16 1/8 1/4
a3 0 0 0 1
ICFTc 7 0 0 1
ICFTe 6 0 2 0
MAFT 4 4 0 0
Table 2: Metrics for non-isomorphic 36 run 33 designs, designs 23 and 24.
0 1/48 1/12 1/6
a3 0 0 0 1
ICFTc 6 0 2 0
ICFTe 0 8 0 0
MAFT 0 8 0 0
0 1/16 1/8
a3 0 0 1
ICFTc 7 0 1
ICFTe 7 0 1
MAFT 6 2 0

Coding invariant cross product matrix for columns 13 to 15 of Taguchi L36

The design was reordered such that the first column changes slowest, the last fastest.

Table 3: Coding invariant cross product matrix for columns 13 to 15 of Taguchi L36 (design 20 of the 24 non-isomorphic ones)
A B C D E F G H J K L M N O P Q R S T U V W X Y Z a b c d e f g h j k l
A 8 8 8 -4 -4 2 2 2 2 2 2 2 -4 2 2 2 -1 -1 -1 -1 2 2 2 -1 2 2 2 2 2 2 2 -1 2 -1 -1 -1
B 8 8 8 -4 -4 2 2 2 2 2 2 2 -4 2 2 2 -1 -1 -1 -1 2 2 2 -1 2 2 2 2 2 2 2 -1 2 -1 -1 -1
C 8 8 8 -4 -4 2 2 2 2 2 2 2 -4 2 2 2 -1 -1 -1 -1 2 2 2 -1 2 2 2 2 2 2 2 -1 2 -1 -1 -1
D -4 -4 -4 8 2 2 2 2 -4 -4 -4 2 2 2 2 2 2 2 2 -1 -1 -1 -1 2 -4 -4 -4 2 -1 -1 -1 2 -1 -1 -1 -1
E -4 -4 -4 2 8 -4 -4 -4 2 2 2 2 2 -1 -1 -1 2 2 2 2 2 2 2 -1 -1 -1 -1 -1 -4 -4 -4 2 2 -1 -1 -1
F 2 2 2 2 -4 8 8 8 2 2 2 -4 -1 2 2 2 2 2 2 -4 -1 -1 -1 -1 -1 -1 -1 2 2 2 2 2 -1 2 2 2
G 2 2 2 2 -4 8 8 8 2 2 2 -4 -1 2 2 2 2 2 2 -4 -1 -1 -1 -1 -1 -1 -1 2 2 2 2 2 -1 2 2 2
H 2 2 2 2 -4 8 8 8 2 2 2 -4 -1 2 2 2 2 2 2 -4 -1 -1 -1 -1 -1 -1 -1 2 2 2 2 2 -1 2 2 2
J 2 2 2 -4 2 2 2 2 8 8 8 -4 -1 -1 -1 -1 2 2 2 -1 2 2 2 -4 2 2 2 -1 -1 -1 -1 2 2 2 2 2
K 2 2 2 -4 2 2 2 2 8 8 8 -4 -1 -1 -1 -1 2 2 2 -1 2 2 2 -4 2 2 2 -1 -1 -1 -1 2 2 2 2 2
L 2 2 2 -4 2 2 2 2 8 8 8 -4 -1 -1 -1 -1 2 2 2 -1 2 2 2 -4 2 2 2 -1 -1 -1 -1 2 2 2 2 2
M 2 2 2 2 2 -4 -4 -4 -4 -4 -4 8 -1 2 2 2 -1 -1 -1 2 2 2 2 2 -1 -1 -1 2 -1 -1 -1 -1 2 -4 -4 -4
N -4 -4 -4 2 2 -1 -1 -1 -1 -1 -1 -1 8 -4 -4 -4 2 2 2 2 -4 -4 -4 2 2 2 2 2 2 2 2 -1 2 -1 -1 -1
O 2 2 2 2 -1 2 2 2 -1 -1 -1 2 -4 8 8 8 2 2 2 -4 2 2 2 2 2 2 2 -4 -1 -1 -1 -1 -1 2 2 2
P 2 2 2 2 -1 2 2 2 -1 -1 -1 2 -4 8 8 8 2 2 2 -4 2 2 2 2 2 2 2 -4 -1 -1 -1 -1 -1 2 2 2
Q 2 2 2 2 -1 2 2 2 -1 -1 -1 2 -4 8 8 8 2 2 2 -4 2 2 2 2 2 2 2 -4 -1 -1 -1 -1 -1 2 2 2
R -1 -1 -1 2 2 2 2 2 2 2 2 -1 2 2 2 2 8 8 8 -4 2 2 2 -4 2 2 2 -1 2 2 2 -4 -1 -1 -1 -1
S -1 -1 -1 2 2 2 2 2 2 2 2 -1 2 2 2 2 8 8 8 -4 2 2 2 -4 2 2 2 -1 2 2 2 -4 -1 -1 -1 -1
T -1 -1 -1 2 2 2 2 2 2 2 2 -1 2 2 2 2 8 8 8 -4 2 2 2 -4 2 2 2 -1 2 2 2 -4 -1 -1 -1 -1
U -1 -1 -1 -1 2 -4 -4 -4 -1 -1 -1 2 2 -4 -4 -4 -4 -4 -4 8 2 2 2 2 -1 -1 -1 2 2 2 2 2 -1 2 2 2
V 2 2 2 -1 2 -1 -1 -1 2 2 2 2 -4 2 2 2 2 2 2 2 8 8 8 -4 -1 -1 -1 -1 2 2 2 -1 -4 2 2 2
W 2 2 2 -1 2 -1 -1 -1 2 2 2 2 -4 2 2 2 2 2 2 2 8 8 8 -4 -1 -1 -1 -1 2 2 2 -1 -4 2 2 2
X 2 2 2 -1 2 -1 -1 -1 2 2 2 2 -4 2 2 2 2 2 2 2 8 8 8 -4 -1 -1 -1 -1 2 2 2 -1 -4 2 2 2
Y -1 -1 -1 2 -1 -1 -1 -1 -4 -4 -4 2 2 2 2 2 -4 -4 -4 2 -4 -4 -4 8 2 2 2 -1 -1 -1 -1 2 2 2 2 2
Z 2 2 2 -4 -1 -1 -1 -1 2 2 2 -1 2 2 2 2 2 2 2 -1 -1 -1 -1 2 8 8 8 -4 2 2 2 -4 2 2 2 2
a 2 2 2 -4 -1 -1 -1 -1 2 2 2 -1 2 2 2 2 2 2 2 -1 -1 -1 -1 2 8 8 8 -4 2 2 2 -4 2 2 2 2
b 2 2 2 -4 -1 -1 -1 -1 2 2 2 -1 2 2 2 2 2 2 2 -1 -1 -1 -1 2 8 8 8 -4 2 2 2 -4 2 2 2 2
c 2 2 2 2 -1 2 2 2 -1 -1 -1 2 2 -4 -4 -4 -1 -1 -1 2 -1 -1 -1 -1 -4 -4 -4 8 2 2 2 2 2 -4 -4 -4
d 2 2 2 -1 -4 2 2 2 -1 -1 -1 -1 2 -1 -1 -1 2 2 2 2 2 2 2 -1 2 2 2 2 8 8 8 -4 -4 2 2 2
e 2 2 2 -1 -4 2 2 2 -1 -1 -1 -1 2 -1 -1 -1 2 2 2 2 2 2 2 -1 2 2 2 2 8 8 8 -4 -4 2 2 2
f 2 2 2 -1 -4 2 2 2 -1 -1 -1 -1 2 -1 -1 -1 2 2 2 2 2 2 2 -1 2 2 2 2 8 8 8 -4 -4 2 2 2
g -1 -1 -1 2 2 2 2 2 2 2 2 -1 -1 -1 -1 -1 -4 -4 -4 2 -1 -1 -1 2 -4 -4 -4 2 -4 -4 -4 8 2 2 2 2
h 2 2 2 -1 2 -1 -1 -1 2 2 2 2 2 -1 -1 -1 -1 -1 -1 -1 -4 -4 -4 2 2 2 2 2 -4 -4 -4 2 8 -4 -4 -4
j -1 -1 -1 -1 -1 2 2 2 2 2 2 -4 -1 2 2 2 -1 -1 -1 2 2 2 2 2 2 2 2 -4 2 2 2 2 -4 8 8 8
k -1 -1 -1 -1 -1 2 2 2 2 2 2 -4 -1 2 2 2 -1 -1 -1 2 2 2 2 2 2 2 2 -4 2 2 2 2 -4 8 8 8
l -1 -1 -1 -1 -1 2 2 2 2 2 2 -4 -1 2 2 2 -1 -1 -1 2 2 2 2 2 2 2 2 -4 2 2 2 2 -4 8 8 8

The 12 non-isomorphic GMA 36 run 63 designs

These designs have been obtained from the Website by Eendebak and Schoen (2010). All these designs are regular in all three senses of Grömping and Bailey (2016), which can be seen from the facts that the ARFTs from these designs consist of ones only, which implies R2 regularity and CC regularity, and that there are only three factors so that CC regularity implies geometric regularity.

Table 4: Metrics for non-isomorphic 36 run 63 designs, designs 1 to 4.
0 5
a3 0 1
ICFTc 124 1
ICFTe 124 1
0 5
a3 0 1
ICFTc 124 1
ICFTe 124 1
0 5
a3 0 1
ICFTc 124 1
ICFTe 124 1
0 5
a3 0 1
ICFTc 124 1
ICFTe 124 1
Table 4: Metrics for non-isomorphic 36 run 63 designs, designs 5 to 8.
0 5
a3 0 1
ICFTc 124 1
ICFTe 124 1
0 5
a3 0 1
ICFTc 124 1
ICFTe 124 1
0 5
a3 0 1
ICFTc 124 1
ICFTe 124 1
0 5
a3 0 1
ICFTc 124 1
ICFTe 124 1
Table 4: Metrics for non-isomorphic 36 run 63 designs, designs 9 to 12.
0 5
a3 0 1
ICFTc 124 1
ICFTe 124 1
0 5
a3 0 1
ICFTc 124 1
ICFTe 124 1
0 5
a3 0 1
ICFTc 124 1
ICFTe 124 1
0 5
a3 0 1
ICFTc 124 1
ICFTe 124 1

The 10 non-isomorphic GMA 32 run 43 designs

These designs have been obtained from the Website by Eendebak and Schoen (2010).

Table 5: Metrics for non-isomorphic 32 run 43 designs, designs 1 to 4.
0 1/19 1
a3 0 0 1
ICFTc 26 0 1
ICFTe 8 19 0
0 1/13 1
a3 0 0 1
ICFTc 26 0 1
ICFTe 14 13 0
0 1/15 1
a3 0 0 1
ICFTc 26 0 1
ICFTe 12 15 0
0 1/11 1
a3 0 0 1
ICFTc 26 0 1
ICFTe 16 11 0
Table 5: Metrics for non-isomorphic 32 run 43 designs, designs 5 to 8.
0 1/9 1
a3 0 0 1
ICFTc 26 0 1
ICFTe 18 9 0
0 1/13 1
a3 0 0 1
ICFTc 26 0 1
ICFTe 14 13 0
0 1/9 1
a3 0 0 1
ICFTc 26 0 1
ICFTe 18 9 0
0 1/9 1
a3 0 0 1
ICFTc 26 0 1
ICFTe 18 9 0
Table 5: Metrics for non-isomorphic 32 run 43 designs, designs 9 to 12.
0 1/7 1
a3 0 0 1
ICFTc 26 0 1
ICFTe 20 7 0
0 1/13 1
a3 0 0 1
ICFTc 26 0 1
ICFTe 14 13 0

The following table also shows the SCFTs for these designs; these were proposed in Grömping (in press) for detecting non-isomorphism, using these designs as an example: all of them can be distinguished by SCFTs. SCFTs were also used by Grömping and Bailey for regularity assessment. Only the first design is CC regular (and geometrically regular) but not R2 regular (average R2 is 1/3).

Table 6: SCFTs for the 32 run 43 designs
0 1/4 3/8 1/2 5/8 3/4 1
1 6 0 0 0 0 0 3
2 3 3 0 0 0 3 0
3 4 0 0 4 0 0 1
4 2 3 0 3 0 1 0
5 1 4 1 2 1 0 0
6 3 0 0 6 0 0 0
7 2 2 0 5 0 0 0
8 1 4 0 4 0 0 0
9 0 3 6 0 0 0 0
10 3 0 0 6 0 0 0

The 20 non-isomorphic GMA 32 run 49 designs

These designs have been obtained from the Website by Eendebak and Schoen (2010).

Table 7: Metrics for non-isomorphic 32 run 49 designs, design 1.
0 1/19 1 3 92
a3 0 0 0 0 1
ICFTc 2184 0 80 4 0
ICFTe 744 1520 0 4 0
Table 7: Metrics for non-isomorphic 32 run 49 designs, design 2.
0 1/19 1 3 92
a3 0 0 0 0 1
ICFTc 2184 0 80 4 0
ICFTe 744 1520 0 4 0
Table 7: Metrics for non-isomorphic 32 run 49 designs, design 3.
0 1/19 1 3 92
a3 0 0 0 0 1
ICFTc 2184 0 80 4 0
ICFTe 744 1520 0 4 0
Table 7: Metrics for non-isomorphic 32 run 49 designs, design 4.
0 1/19 1 3 92
a3 0 0 0 0 1
ICFTc 2184 0 80 4 0
ICFTe 744 1520 0 4 0
Table 7: Metrics for non-isomorphic 32 run 49 designs, design 5.
0 1/19 1/15 1/13 0.106 1 1.894 3 92
a3 0 0 0 0 0 0 0 0 1
ICFTc 2180 0 0 0 4 78 4 2 0
ICFTe 856 1178 120 104 4 0 4 2 0
Table 7: Metrics for non-isomorphic 32 run 49 designs, design 6.
0 1/19 1/15 1/13 0.106 1 1.894 3 92
a3 0 0 0 0 0 0 0 0 1
ICFTc 2180 0 0 0 4 78 4 2 0
ICFTe 856 1178 120 104 4 0 4 2 0
Table 7: Metrics for non-isomorphic 32 run 49 designs, design 7.
0 1/19 1/15 1/13 0.106 1 1.894 3 92
a3 0 0 0 0 0 0 0 0 1
ICFTc 2180 0 0 0 4 78 4 2 0
ICFTe 856 1178 120 104 4 0 4 2 0
Table 7: Metrics for non-isomorphic 32 run 49 designs, design 8.
0 0.049 1/19 1/16 1/15 1/13 1/4 3/10 1 1.201 3/2 3 92
a3 0 0 0 0 0 0 0 0 0 0 0 0 1
ICFTc 2176 4 0 0 0 0 4 0 74 4 4 2 0
ICFTe 1056 4 570 16 180 416 0 20 0 4 0 2 0
Table 7: Metrics for non-isomorphic 32 run 49 designs, design 9.
0 0.049 1/19 1/16 1/15 1/13 0.106 1/4 3/10 1 1.201 3/2 1.894 92
a3 0 0 0 0 0 0 0 0 0 0 0 0 0 1
ICFTc 2169 5 0 0 0 0 5 5 0 73 5 1 5 0
ICFTe 1096 5 475 20 210 442 5 0 5 0 5 0 5 0
Table 7: Metrics for non-isomorphic 32 run 49 designs, design 10.
0 0.049 1/19 1/16 1/15 1/13 0.106 1/4 3/10 1 1.201 3/2 1.894 92
a3 0 0 0 0 0 0 0 0 0 0 0 0 0 1
ICFTc 2163 9 0 0 0 0 3 9 0 71 9 1 3 0
ICFTe 1118 9 437 36 180 468 3 0 5 0 9 0 3 0
Table 7: Metrics for non-isomorphic 32 run 49 designs, design 11.
0 0 0.03 1/24 0.049 1/19 1/18 1/16 1/15 1/13 1/11 0.106 0.107 1/9 1/4 3/10 0.317 1/3 0.714 1 1.183 1.201 3/2 1.894 92
a3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
ICFTc 2145 4 4 0 7 0 0 4 0 0 0 1 4 0 7 0 4 4 4 67 4 7 1 1 0
ICFTe 1170 4 4 12 7 361 24 24 210 364 22 1 4 36 0 5 4 0 4 0 4 7 0 1 0
Table 7: Metrics for non-isomorphic 32 run 49 designs, design 12.
0 0 0 0 0 0.013 0.039 1/24 0.049 1/19 1/16 1/15 0.072 1/13 0.083 1/12 1/11 0.103 0.106 1/9 1/8 0.246 1/4 0.279 3/10 0.317 3/8 0.662 0.745 3/4 1 1.183 1.201 3/2 1.894 92
a3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
ICFTc 2114 4 4 4 2 4 4 0 7 0 0 0 4 0 4 0 0 4 1 0 8 2 13 4 0 1 0 4 2 4 64 1 7 1 1 0
ICFTe 1207 4 4 4 2 4 4 24 7 342 28 90 4 364 4 12 66 4 1 54 4 2 0 4 5 1 8 4 2 0 0 1 7 0 1 0
Table 7: Metrics for non-isomorphic 32 run 49 designs, design 13.
0 0 1/24 0.049 1/19 1/16 1/15 1/13 1/12 1/11 0.106 1/9 1/8 0.246 1/4 3/10 0.317 3/8 0.745 3/4 1 1.183 1.201 3/2 1.894 92
a3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
ICFTc 2150 2 0 5 0 0 0 0 0 0 1 0 8 2 11 0 5 0 2 4 66 5 5 1 1 0
ICFTe 1221 2 12 5 342 28 150 338 12 66 1 54 4 2 0 5 5 8 2 0 0 5 5 0 1 0
Table 7: Metrics for non-isomorphic 32 run 49 designs, design 14.
0 0.049 1/19 1/16 1/15 1/13 0.106 1/4 3/10 1 1.201 3/2 1.894 92
a3 0 0 0 0 0 0 0 0 0 0 0 0 0 1
ICFTc 2166 8 0 0 0 0 2 8 0 70 8 4 2 0
ICFTe 1142 8 418 32 90 546 2 0 20 0 8 0 2 0
Table 7: Metrics for non-isomorphic 32 run 49 designs, design 15.
0 1/19 1/13 0.106 1 1.894 92
a3 0 0 0 0 0 0 1
ICFTc 2176 0 0 8 76 8 0
ICFTe 904 1140 208 8 0 8 0
Table 7: Metrics for non-isomorphic 32 run 49 designs, design 16.
0 0.049 1/19 1/16 1/15 1/13 0.106 1/4 3/10 1 1.201 3/2 1.894 92
a3 0 0 0 0 0 0 0 0 0 0 0 0 0 1
ICFTc 2172 4 0 0 0 0 4 4 0 72 4 4 4 0
ICFTe 1168 4 304 16 120 624 4 0 20 0 4 0 4 0
Table 7: Metrics for non-isomorphic 32 run 49 designs, design 17.
0 0.049 1/19 1/16 1/15 1/13 1/11 0.106 1/9 1/4 3/10 1 1.201 3/2 1.894 92
a3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
ICFTc 2172 4 0 0 0 0 0 4 0 4 0 72 4 4 4 0
ICFTe 1196 4 342 16 120 416 88 4 54 0 20 0 4 0 4 0
Table 7: Metrics for non-isomorphic 32 run 49 designs, design 18.
0 1/24 0.049 1/19 1/16 1/15 1/13 1/11 0.106 1/9 1/4 3/10 1 1.201 3/2 1.894 92
a3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
ICFTc 2166 0 8 0 0 0 0 0 2 0 8 0 70 8 4 2 0
ICFTe 1174 24 8 380 16 120 416 44 2 54 0 20 0 8 0 2 0
Table 7: Metrics for non-isomorphic 32 run 49 designs, design 19.
0 1/19 1/13 0.317 1 1.183 92
a3 0 0 0 0 0 0 1
ICFTc 2168 0 0 16 68 16 0
ICFTe 1016 1064 156 16 0 16 0
Table 7: Metrics for non-isomorphic 32 run 49 designs, design 20.
0 0.049 1/19 1/16 1/15 1/13 1/4 3/10 1 1.201 3/2 92
a3 0 0 0 0 0 0 0 0 0 0 0 1
ICFTc 2160 12 0 0 0 0 12 0 68 12 4 0
ICFTe 1144 12 380 48 210 442 0 20 0 12 0 0

The next table shows the SCFTs for the designs; apart from two groups with identical patterns, the designs can all be distinguished by SCFTs. One of the identical groups consists of the first four designs, which are CC regular but not R2 regular (some average R2 values are “1”, but most are 1/3); geometric regularity has not been assessed.

Table 8: SCFTs for the 32 run 49 designs
0 1/8 9/50 0.198 1/4 0.323 3/8 1/2 0.552 5/8 0.677 0.695 3/4 1
1 480 0 0 0 0 0 0 0 0 0 0 0 0 276
2 480 0 0 0 0 0 0 0 0 0 0 0 0 276
3 480 0 0 0 0 0 0 0 0 0 0 0 0 276
4 480 0 0 0 0 0 0 0 0 0 0 0 0 276
5 432 0 0 0 0 0 0 96 0 0 0 0 0 228
6 432 0 0 0 0 0 0 96 0 0 0 0 0 228
7 432 0 0 0 0 0 0 96 0 0 0 0 0 228
8 324 0 0 0 8 0 0 296 0 0 0 0 8 120
9 313 0 0 0 10 0 0 314 0 0 0 0 10 109
10 297 0 0 0 18 0 0 330 0 0 0 0 18 93
11 265 0 4 8 42 0 4 324 8 0 0 4 18 79
12 242 2 2 8 68 4 12 305 8 8 4 2 24 67
13 252 2 2 0 66 0 12 319 0 8 0 2 18 75
14 284 0 0 0 16 0 0 360 0 0 0 0 16 80
15 416 0 0 0 0 0 0 128 0 0 0 0 0 212
16 276 0 0 0 8 0 0 392 0 0 0 0 8 72
17 266 0 0 0 48 0 0 344 0 0 0 0 24 74
18 268 0 0 0 48 0 0 336 0 0 0 0 32 72
19 372 0 0 0 32 0 0 168 0 0 0 0 0 184
20 278 0 0 0 24 0 0 356 0 0 0 0 24 74

References

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Cheng, S.-W. and Ye, K.Q. (2004). Geometric isomorphism and minimum aberration for factorial designs with quantitative factors. The Annals of Statistics 32, 2168-2185.

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Grömping, U. (in press). Frequency tables for the coding invariant quality assessment of factorial designs. IISE Transactions.

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