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The columns of the arrays are balanced and orthogonal. This means that in each pair of columns, all factor combinations occur the same number of times. Orthogonal designs let you estimate the effect of each factor on the response independently of all other factors.

The notation L(runs) (levels ^ factors) indicates the following:
  • L(runs) = number of runs
  • (levels ^ factors) = number of levels for each factor ^ number of factors

For example, an L8 design has 8 runs. (2^3) or (2 3) means 3 factors at 2 levels.

If your notation is L(runs) (number ^ exponent number ^ exponent) then you have a mixed-level design. For example, an L18 (2^1 3^7) means that the design has 18 runs, 1 factor with 2 levels, and 7 factors with 3 levels.

L4 (23)

  1 2 3
1 1 1 1
2 1 2 2
3 2 1 2
4 2 2 1

L8 (27)

  1 2 3 4 5 6 7
1 1 1 1 1 1 1 1
2 1 1 1 2 2 2 2
3 1 2 2 1 1 2 2
4 1 2 2 2 2 1 1
5 2 1 2 1 2 1 2
6 2 1 2 2 1 2 1
7 2 2 1 1 2 2 1
8 2 2 1 2 1 1 2

L8 (24), (41)

  1 2 3 4 5
1 1 1 1 1 1
2 1 2 2 2 2
3 2 1 1 2 2
4 2 2 2 1 1
5 3 1 2 1 2
6 3 2 1 2 1
7 4 1 2 2 1
8 4 2 1 1 2

L9 (34)

  1 2 3 4
1 1 1 1 1
2 1 2 2 2
3 1 3 3 3
4 2 1 2 3
5 2 2 3 1
6 2 3 1 2
7 3 1 3 2
8 3 2 1 3
9 3 3 2 1

L12 (211)

  1 2 3 4 5 6 7 8 9 10 11
1 1 1 1 1 1 1 1 1 1 1 1
2 1 1 1 1 1 2 2 2 2 2 2
3 1 1 2 2 2 1 1 1 2 2 2
4 1 2 1 2 2 1 2 2 1 1 2
5 1 2 2 1 2 2 1 2 1 2 1
6 1 2 2 2 1 2 2 1 2 1 1
7 2 1 2 2 1 1 2 2 1 2 1
8 2 1 2 1 2 2 2 1 1 1 2
9 2 1 1 2 2 2 1 2 2 1 1
10 2 2 2 1 1 1 1 2 2 1 2
11 2 2 1 2 1 2 1 1 1 2 2
12 2 2 1 1 2 1 2 1 2 2 1

L16 (215)

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
2 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2
3 1 1 1 2 2 2 2 1 1 1 1 2 2 2 2
4 1 1 1 2 2 2 2 2 2 2 2 1 1 1 1
5 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2
6 1 2 2 1 1 2 2 2 2 1 1 2 2 1 1
7 1 2 2 2 2 1 1 1 1 2 2 2 2 1 1
8 1 2 2 2 2 1 1 2 2 1 1 1 1 2 2
9 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2
10 2 1 2 1 2 1 2 2 1 2 1 2 1 2 1
11 2 1 2 2 1 2 1 1 2 1 2 2 1 2 1
12 2 1 2 2 1 2 1 2 1 2 1 1 2 1 2
13 2 2 1 1 2 2 1 1 2 2 1 1 2 1 2
14 2 2 1 1 2 2 1 2 1 1 2 2 1 1 2
15 2 2 1 2 1 1 2 1 2 2 1 2 1 1 2
16 2 2 1 2 1 1 2 2 1 1 2 1 2 2 1

L16 (212), (41)

  1 2 3 4 5 6 7 8 9 10 11 12 13
1 1 1 1 1 1 1 1 1 1 1 1 1 1
2 1 1 1 1 1 2 2 2 2 2 2 2 2
3 1 2 2 2 2 1 1 1 1 2 2 2 2
4 1 2 2 2 2 2 2 2 2 1 1 1 1
5 2 1 1 2 2 1 1 2 2 1 1 2 2
6 2 1 1 2 2 2 2 1 1 2 2 1 1
7 2 2 2 1 1 1 1 2 2 2 2 1 1
8 2 2 2 1 1 2 2 1 1 1 1 2 2
9 3 1 2 1 2 1 2 1 2 1 2 1 2
10 3 1 2 1 2 2 1 2 1 2 1 2 1
11 3 2 1 2 1 1 2 1 2 2 1 2 1
12 3 2 1 2 1 2 1 2 1 1 2 1 2
13 4 1 2 2 1 1 2 2 1 1 2 2 1
14 4 1 2 2 1 2 1 1 2 2 1 1 2
15 4 2 1 1 2 1 2 2 1 2 1 1 2
16 4 2 1 1 2 2 1 1 2 1 2 2 1

L16 (29), (42)

  1 2 3 4 5 6 7 8 9 10 11
1 1 1 1 1 1 1 1 1 1 1 1
2 1 2 1 1 1 2 2 2 2 2 2
3 1 3 2 2 2 1 1 1 2 2 2
4 1 4 2 2 2 2 2 2 1 1 1
5 2 1 1 2 2 1 2 2 1 2 2
6 2 2 1 2 2 2 1 1 2 1 1
7 2 3 2 1 1 1 2 2 2 1 1
8 2 4 2 1 1 2 1 1 1 2 2
9 3 1 2 1 2 2 1 2 2 1 2
10 3 2 2 1 2 1 2 1 1 2 1
11 3 3 1 2 1 2 1 2 1 2 1
12 3 4 1 2 1 1 2 1 2 1 2
13 4 1 2 2 1 2 2 1 2 2 1
14 4 2 2 2 1 1 1 2 1 1 2
15 4 3 1 1 2 2 2 1 1 1 2
16 4 4 1 1 2 1 1 2 2 2 1

L16 (26), (43)

  1 2 3 4 5 6 7 8 9
1 1 1 1 1 1 1 1 1 1
2 1 2 2 1 1 2 2 2 2
3 1 3 3 2 2 1 1 2 2
4 1 4 4 2 2 2 2 1 1
5 2 1 2 2 2 1 2 1 2
6 2 2 1 2 2 2 1 2 1
7 2 3 4 1 1 1 2 2 1
8 2 4 3 1 1 2 1 1 2
9 3 1 3 1 2 2 2 2 1
10 3 2 4 1 2 1 1 1 2
11 3 3 1 2 1 2 2 1 2
12 3 4 2 2 1 1 1 2 1
13 4 1 4 2 1 2 1 2 2
14 4 2 3 2 1 1 2 1 1
15 4 3 2 1 2 2 1 1 1
16 4 4 1 1 2 1 2 2 2

L16 (23), (44)

  1 2 3 4 5 6 7
1 1 1 1 1 1 1 1
2 1 2 2 1 2 2 2
3 1 3 3 2 3 1 2
4 1 4 4 2 4 2 1
5 2 1 2 2 1 2 1
6 2 2 1 2 2 1 2
7 2 3 4 1 3 2 2
8 2 4 3 1 4 1 1
9 3 1 3 1 4 2 2
10 3 2 4 1 3 1 1
11 3 3 1 2 2 2 1
12 3 4 2 2 1 1 2
13 4 1 4 2 2 1 2
14 4 2 3 2 1 2 1
15 4 3 2 1 4 1 1
16 4 4 1 1 3 2 2

L16 (45)

  1 2 3 4 5
1 1 1 1 1 1
2 1 2 2 2 2
3 1 3 3 3 3
4 1 4 4 4 4
5 2 1 2 3 4
6 2 2 1 4 3
7 2 3 4 1 2
8 2 4 3 2 1
9 3 1 3 4 2
10 3 2 4 3 1
11 3 3 1 2 4
12 3 4 2 1 3
13 4 1 4 2 3
14 4 2 3 1 4
15 4 3 2 4 1
16 4 4 1 3 2

L16 (81), (28)

  1 2 3 4 5 6 7 8 9
1 1 1 1 1 1 1 1 1 1
2 1 2 2 2 2 2 2 2 2
3 2 1 1 1 1 2 2 2 2
4 2 2 2 2 2 1 1 1 1
5 3 1 1 2 2 1 1 2 2
6 3 2 2 1 1 2 2 1 1
7 4 1 1 2 2 2 2 1 1
8 4 2 2 1 1 1 1 2 2
9 5 1 2 1 2 1 2 1 2
10 5 2 1 2 1 2 1 2 1
11 6 1 2 1 2 2 1 2 1
12 6 2 1 2 1 1 2 1 2
13 7 1 2 2 1 1 2 2 1
14 7 2 1 1 2 2 1 1 2
15 8 1 2 2 1 2 1 1 2
16 8 2 1 1 2 1 2 2 1

L18 (21), (37)

  1 2 3 4 5 6 7 9
1 1 1 1 1 1 1 1 1
2 1 1 2 2 2 2 2 2
3 1 1 3 3 3 3 3 3
4 1 2 1 1 2 2 3 2
5 1 2 2 2 3 3 1 3
6 1 2 3 3 1 1 2 1
7 1 3 1 2 1 3 2 3
8 1 3 2 3 2 1 3 1
9 1 3 3 1 3 2 1 2
10 2 1 1 3 3 2 2 1
11 2 1 2 1 1 3 3 2
12 2 1 3 2 2 1 1 3
13 2 2 1 2 3 1 3 2
14 2 2 2 3 1 2 1 3
15 2 2 3 1 2 3 2 1
16 2 3 1 3 2 3 1 2
17 2 3 2 1 3 1 2 3
18 2 3 3 2 1 2 3 1

L18 (61), (36)

  1 2 3 4 5 6 7
1 1 1 1 1 1 1 1
2 1 2 2 2 2 2 2
3 1 3 3 3 3 3 3
4 2 1 1 2 2 3 3
5 2 2 2 3 3 1 1
6 2 3 3 1 1 2 2
7 3 1 2 1 3 2 3
8 3 2 3 2 1 3 1
9 3 3 1 3 2 1 2
10 4 1 3 3 2 2 1
11 4 2 1 1 3 3 2
12 4 3 2 2 1 1 3
13 5 1 2 3 1 3 2
14 5 2 3 1 2 1 3
15 5 3 1 2 3 2 1
16 6 1 3 2 3 1 2
17 6 2 1 3 1 2 3
18 6 3 2 1 2 3 1

L25 (56)

  1 2 3 4 5 6
1 1 1 1 1 1 1
2 1 2 2 2 2 2
3 1 3 3 3 3 3
4 1 4 4 4 4 4
5 1 5 5 5 5 5
6 2 1 2 3 4 5
7 2 2 3 4 5 1
8 2 3 4 5 1 2
9 2 4 5 1 2 3
10 2 5 1 2 3 4
11 3 1 3 5 2 4
12 3 2 4 1 3 5
13 3 3 5 2 4 1
14 3 4 1 3 5 2
15 3 5 2 4 1 3
16 4 1 4 2 5 3
17 4 2 5 3 1 4
18 4 3 1 4 2 5
19 4 4 2 5 3 1
20 4 5 3 1 4 2
21 5 1 5 4 3 2
22 5 2 1 5 4 3
23 5 3 2 1 5 4
24 5 4 3 2 1 5
25 5 5 4 3 2 1

L27 (313)

  1 2 3 4 5 6 7 8 9 10 11 12 13
1 1 1 1 1 1 1 1 1 1 1 1 1 1
2 1 1 1 1 2 2 2 2 2 2 2 2 2
3 1 1 1 1 3 3 3 3 3 3 3 3 3
4 1 2 2 2 1 1 1 2 2 2 3 3 3
5 1 2 2 2 2 2 2 3 3 3 1 1 1
6 1 2 2 2 3 3 3 1 1 1 2 2 2
7 1 3 3 3 1 1 1 3 3 3 2 2 2
8 1 3 3 3 2 2 2 1 1 1 3 3 3
9 1 3 3 3 3 3 3 2 2 2 1 1 1
10 2 1 2 3 1 2 3 1 2 3 1 2 3
11 2 1 2 3 2 3 1 2 3 1 2 3 1
12 2 1 2 3 3 1 2 3 1 2 3 1 2
13 2 2 3 1 1 2 3 2 3 1 3 1 2
14 2 2 3 1 2 3 1 3 1 2 1 2 3
15 2 2 3 1 3 1 2 1 2 3 2 3 1
16 2 3 1 2 1 2 3 3 1 2 2 3 1
17 2 3 1 2 2 3 1 1 2 3 3 1 2
18 2 3 1 2 3 1 2 2 3 1 1 2 3
19 3 1 3 2 1 3 2 1 3 2 1 3 2
20 3 1 3 2 2 1 3 2 1 3 2 1 3
21 3 1 3 2 3 2 1 3 2 1 3 2 1
22 3 2 1 3 1 3 2 2 1 3 3 2 1
23 3 2 1 3 2 1 3 3 2 1 1 3 2
24 3 2 1 3 3 2 1 1 3 2 2 1 3
25 3 3 2 1 1 3 2 3 2 1 2 1 3
26 3 3 2 1 2 1 3 1 3 2 3 2 1
27 3 3 2 1 3 2 1 2 1 3 1 3 2

L32 (231)

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2
3 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 1
4 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2
5 1 1 1 2 2 2 2 1 1 1 1 2 2 2 2 1
6 1 1 1 2 2 2 2 1 1 1 1 2 2 2 2 2
7 1 1 1 2 2 2 2 2 2 2 2 1 1 1 1 1
8 1 1 1 2 2 2 2 2 2 2 2 1 1 1 1 2
9 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1
10 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2 2
11 1 2 2 1 1 2 2 2 2 1 1 2 2 1 1 1
12 1 2 2 1 1 2 2 2 2 1 1 2 2 1 1 2
13 1 2 2 2 2 1 1 1 1 2 2 2 2 1 1 1
14 1 2 2 2 2 1 1 1 1 2 2 2 2 1 1 2
15 1 2 2 2 2 1 1 2 2 1 1 1 1 2 2 1
16 1 2 2 2 2 1 1 2 2 1 1 1 1 2 2 2
17 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1
18 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 2
19 2 1 2 1 2 1 2 2 1 2 1 2 1 2 1 1
20 2 1 2 1 2 1 2 2 1 2 1 2 1 2 1 2
21 2 1 2 2 1 2 1 1 2 1 2 2 1 2 1 1
22 2 1 2 2 1 2 1 1 2 1 2 2 1 2 1 2
23 2 1 2 2 1 2 1 2 1 2 1 1 2 1 2 1
24 2 1 2 2 1 2 1 2 1 2 1 1 2 1 2 2
25 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1
26 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1 2
27 2 2 1 1 2 2 1 2 1 1 2 2 1 1 2 1
28 2 2 1 1 2 2 1 2 1 1 2 2 1 1 2 2
29 2 2 1 2 1 1 2 1 2 2 1 2 1 1 2 1
30 2 2 1 2 1 1 2 1 2 2 1 2 1 1 2 2
31 2 2 1 2 1 1 2 2 1 1 2 1 2 2 1 1
32 2 2 1 2 1 1 2 2 1 1 2 1 2 2 1 2
  17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
3 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2
42 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1
5 1 1 1 2 2 2 2 1 1 1 1 2 2 2 2
6 2 2 2 1 1 1 1 2 2 2 2 1 1 1 1
7 1 1 1 2 2 2 2 2 2 2 2 1 1 1 1
8 2 2 2 1 1 1 1 1 1 1 1 2 2 2 2
9 1 2 2 1 1 2 2 1 1 2 2 1 1 2 2
10 2 1 1 2 2 1 1 2 2 1 1 2 2 1 1
11 1 2 2 1 1 2 2 2 2 1 1 2 2 1 1
12 2 1 1 2 2 1 1 1 1 2 2 1 1 2 2
13 1 2 2 2 2 1 1 1 1 2 2 2 2 1 1
14 2 1 1 1 1 2 2 2 2 1 1 1 1 2 2
15 1 2 2 2 2 1 1 2 2 1 1 1 1 2 2
16 2 1 1 1 1 2 2 1 1 2 2 2 2 1 1
17 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2
18 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1
19 2 1 2 1 2 1 2 2 1 2 1 2 1 2 1
20 1 2 1 2 1 2 1 1 2 1 2 1 2 1 2
21 2 1 2 2 1 2 1 1 2 1 2 2 1 2 1
22 1 2 1 1 2 1 2 2 1 2 1 1 2 1 2
23 2 1 2 2 1 2 1 2 1 2 1 1 2 1 2
24 1 2 1 1 2 1 2 1 2 1 2 2 1 2 1
25 2 2 1 1 2 2 1 1 2 2 1 1 2 2 1
26 1 1 2 2 1 1 2 2 1 1 2 2 1 1 2
27 2 2 1 1 2 2 1 2 1 1 2 2 1 1 2
28 1 1 2 2 1 1 2 1 2 2 1 1 2 2 1
29 2 2 1 2 1 1 2 1 2 2 1 2 1 1 2
30 1 1 2 1 2 2 1 2 1 1 2 1 2 2 1
31 2 2 1 2 1 1 2 2 1 1 2 1 2 2 1
32 1 1 2 1 2 2 1 1 2 2 1 2 1 1 2

L32 (21), (49)

  1 2 3 4 5 6 7 8 9 10
1 1 1 1 1 1 1 1 1 1 1
2 1 1 2 2 2 2 2 2 2 2
3 1 1 3 3 3 3 3 3 3 3
4 1 1 4 4 4 4 4 4 4 4
5 1 2 1 1 2 2 3 3 4 4
6 1 2 2 2 1 1 4 4 3 3
7 1 2 3 3 4 4 1 1 2 2
8 1 2 4 4 3 3 2 2 1 1
9 1 3 1 2 3 4 1 2 3 4
10 1 3 2 1 4 3 2 1 4 3
11 1 3 3 4 1 2 3 4 1 2
12 1 3 4 3 2 1 4 3 2 1
13 1 4 1 2 4 3 3 4 2 1
14 1 4 2 1 3 4 4 3 1 2
15 1 4 3 4 2 1 1 2 4 3
16 1 4 4 3 1 2 2 1 3 4
17 2 1 1 4 1 4 2 3 2 3
18 2 1 2 3 2 3 1 4 1 4
19 2 1 3 2 3 2 4 1 4 1
20 2 1 4 1 4 1 3 2 3 2
21 2 2 1 4 2 3 4 1 3 2
22 2 2 2 3 1 4 3 2 4 1
23 2 2 3 2 4 1 2 3 1 4
24 2 2 4 1 3 2 1 4 2 3
25 2 3 1 3 3 1 2 4 4 2
26 2 3 2 4 4 2 1 3 3 1
27 2 3 3 1 1 3 4 2 2 4
28 2 3 4 2 2 4 3 1 1 3
29 2 4 1 3 4 2 4 2 1 3
30 2 4 2 4 3 1 3 1 2 4
31 2 4 3 1 2 4 2 4 3 1
32 2 4 4 2 1 3 1 3 4 2

L36 (211), (312)

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
2 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2
3 1 1 1 1 1 1 1 1 1 1 1 3 3 3 3 3 3 3 3 3 3 3 3
4 1 1 1 1 1 2 2 2 2 2 2 1 1 1 1 2 2 2 2 3 3 3 3
5 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 3 3 3 3 1 1 1 1
6 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 1 1 1 1 2 2 2 2
7 1 1 2 2 2 1 1 1 2 2 2 1 1 2 3 1 2 3 3 1 2 2 3
8 1 1 2 2 2 1 1 1 2 2 2 2 2 3 1 2 3 1 1 2 3 3 1
9 1 1 2 2 2 1 1 1 2 2 2 3 3 1 2 3 1 2 2 3 1 1 2
10 1 2 1 2 2 1 2 2 1 1 2 1 1 3 2 1 3 2 3 2 1 3 2
11 1 2 1 2 2 1 2 2 1 1 2 2 2 1 3 2 1 3 1 3 2 1 3
12 1 2 1 2 2 1 2 2 1 1 2 3 3 2 1 3 2 1 2 1 3 2 1
13 1 2 2 1 2 2 1 2 1 2 1 1 2 3 1 3 2 1 3 3 2 1 2
14 1 2 2 1 2 2 1 2 1 2 1 2 3 1 2 1 3 2 1 1 3 2 3
15 1 2 2 1 2 2 1 2 1 2 1 3 1 2 3 2 1 3 2 2 1 3 1
16 1 2 2 2 1 2 2 1 2 1 1 1 2 3 2 1 1 3 2 3 3 2 1
17 1 2 2 2 1 2 2 1 2 1 1 2 3 1 3 2 2 1 3 1 1 3 2
18 1 2 2 2 1 2 2 1 2 1 1 3 1 2 1 3 3 2 1 2 2 1 3
19 2 1 2 2 1 1 2 2 1 2 1 1 2 1 3 3 3 1 2 2 1 2 3
20 2 1 2 2 1 1 2 2 1 2 1 2 3 2 1 1 1 2 3 3 2 3 1
21 2 1 2 2 1 1 2 2 1 2 1 3 1 3 2 2 2 3 1 1 3 1 2
22 2 1 2 1 2 2 2 1 1 1 2 1 2 2 3 3 1 2 1 1 3 3 2
23 2 1 2 1 2 2 2 1 1 1 2 2 3 3 1 1 2 3 2 2 1 1 3
24 2 1 2 1 2 2 2 1 1 1 2 3 1 1 2 2 3 1 3 3 2 2 1
25 2 1 1 2 2 2 1 2 2 1 1 1 3 2 1 2 3 3 1 3 1 2 2
26 2 1 1 2 2 2 1 2 2 1 1 2 1 3 2 3 1 1 2 1 2 3 3
27 2 1 1 2 2 2 1 2 2 1 1 3 2 1 3 1 2 2 3 2 3 1 1
28 2 2 2 1 1 1 1 2 2 1 2 1 3 2 2 2 1 1 3 2 3 1 3
29 2 2 2 1 1 1 1 2 2 1 2 2 1 3 3 3 2 2 1 3 1 2 1
30 2 2 2 1 1 1 1 2 2 1 2 3 2 1 1 1 3 3 2 1 2 3 2
31 2 2 1 2 1 2 1 1 1 2 2 1 3 3 3 2 3 2 2 1 2 1 1
32 2 2 1 2 1 2 1 1 1 2 2 2 1 1 1 3 1 3 3 2 3 2 2
33 2 2 1 2 1 2 1 1 1 2 2 3 2 2 2 1 2 1 1 3 1 3 3
34 2 2 1 1 2 1 2 1 2 2 1 1 3 1 2 3 2 3 1 2 2 3 1
35 2 2 1 1 2 1 2 1 2 2 1 2 1 2 3 1 3 1 2 3 3 1 2
36 2 2 1 1 2 1 2 1 2 2 1 3 2 3 1 2 1 2 3 1 1 2 3

L36 (23), (313)

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
2 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2
3 1 1 1 1 3 3 3 3 3 3 3 3 3 3 3 3
4 1 2 2 1 1 1 1 1 2 2 2 2 3 3 3 3
5 1 2 2 1 2 2 2 2 3 3 3 3 1 1 1 1
6 1 2 2 1 3 3 3 3 1 1 1 1 2 2 2 2
7 2 1 2 1 1 1 2 3 1 2 3 3 1 2 2 3
8 2 1 2 1 2 2 3 1 2 3 1 1 2 3 3 1
9 2 1 2 1 3 3 1 2 3 1 2 2 3 1 1 2
10 2 2 1 1 1 1 3 2 1 3 2 3 2 1 3 2
11 2 2 1 1 2 2 1 3 2 1 3 1 3 2 1 3
12 2 2 1 1 3 3 2 1 3 2 1 2 1 3 2 1
13 1 1 1 2 1 2 3 1 3 2 1 3 3 2 1 2
14 1 1 1 2 2 3 1 2 1 3 2 1 1 3 2 3
15 1 1 1 2 3 1 2 3 2 1 3 2 2 1 3 1
16 1 2 2 2 1 2 3 2 1 1 3 2 3 3 2 1
17 1 2 2 2 2 3 1 3 2 2 1 3 1 1 3 2
18 1 2 2 2 3 1 2 1 3 3 2 1 2 2 1 3
19 2 1 2 2 1 2 1 3 3 3 1 2 2 1 2 3
20 2 1 2 2 2 3 2 1 1 1 2 3 3 2 3 1
21 2 1 2 2 3 1 3 2 2 2 3 1 1 3 1 2
22 2 2 1 2 1 2 2 3 3 1 2 1 1 3 3 2
23 2 2 1 2 2 3 3 1 1 2 3 2 2 1 1 3
24 2 2 1 2 3 1 1 2 2 3 1 3 3 2 2 1
25 1 1 1 3 1 3 2 1 2 3 3 1 3 1 2 2
26 1 1 1 3 2 1 3 2 3 1 1 2 1 2 3 3
27 1 1 1 3 3 2 1 3 1 2 2 3 2 3 1 1
28 1 2 2 3 1 3 2 2 2 1 1 3 2 3 1 3
29 1 2 2 3 2 1 3 3 3 2 2 1 3 1 2 1
30 1 2 2 3 3 2 1 1 1 3 3 2 1 2 3 2
31 2 1 2 3 1 3 3 3 2 3 2 2 1 2 1 1
32 2 1 2 3 2 1 1 1 3 1 3 3 2 3 2 2
33 2 1 2 3 3 2 2 2 1 2 1 1 3 1 3 3
34 2 2 1 3 1 3 1 2 3 2 3 1 2 2 3 1
35 2 2 1 3 2 1 2 3 1 3 1 2 3 3 1 2
36 2 2 1 3 3 2 3 1 2 1 2 3 1 1 2 3

L54 (21), (325)

  1 2 3 4 5 6 7 8 9 10 11 12 13
1 1 1 1 1 1 1 1 1 1 1 1 1 1
2 1 1 1 1 1 1 1 1 2 2 2 2 2
3 1 1 1 1 1 1 1 1 3 3 3 3 3
4 1 1 2 2 2 2 2 2 1 1 1 1 1
5 1 1 2 2 2 2 2 2 2 2 2 2 2
6 1 1 2 2 2 2 2 2 3 3 3 3 3
7 1 1 3 3 3 3 3 3 1 1 1 1 1
8 1 1 3 3 3 3 3 3 2 2 2 2 2
9 1 1 3 3 3 3 3 3 3 3 3 3 3
10 1 2 1 1 2 2 3 3 1 1 2 2 3
11 1 2 1 1 2 2 3 3 2 2 3 3 1
12 1 2 1 1 2 2 3 3 3 3 1 1 2
13 1 2 2 2 3 3 1 1 1 1 2 2 3
14 1 2 2 2 3 3 1 1 2 2 3 3 1
15 1 2 2 2 3 3 1 1 3 3 1 1 2
16 1 2 3 3 1 1 2 2 1 1 2 2 3
17 1 2 3 3 1 1 2 2 2 2 3 3 1
18 1 2 3 3 1 1 2 2 3 3 1 1 2
19 1 3 1 2 1 3 2 3 1 2 1 3 2
20 1 3 1 2 1 3 2 3 2 3 2 1 3
21 1 3 1 2 1 3 2 3 3 1 3 2 1
22 1 3 2 3 2 1 3 1 1 2 1 3 2
23 1 3 2 3 2 1 3 1 2 3 2 1 3
24 1 3 2 3 2 1 3 1 3 1 3 2 1
25 1 3 3 1 3 2 1 2 1 2 1 3 2
26 1 3 3 1 3 2 1 2 2 3 2 1 3
27 1 3 3 1 3 2 1 2 3 1 3 2 1
28 2 1 1 3 3 2 2 1 1 3 3 2 2
29 2 1 1 3 3 2 2 1 2 1 1 3 3
30 2 1 1 3 3 2 2 1 3 2 2 1 1
31 2 1 2 1 1 3 3 2 1 3 3 2 2
32 2 1 2 1 1 3 3 2 2 1 1 3 3
33 2 1 2 1 1 3 3 2 3 2 2 1 1
34 2 1 3 2 2 1 1 3 1 3 3 2 2
35 2 1 3 2 2 1 1 3 2 1 1 3 3
36 2 1 3 2 2 1 1 3 3 2 2 1 1
37 2 2 1 2 3 1 3 2 1 2 3 1 3
38 2 2 1 2 3 1 3 2 2 3 1 2 1
39 2 2 1 2 3 1 3 2 3 1 2 3 2
40 2 2 2 3 1 2 1 3 1 2 3 1 3
41 2 2 2 3 1 2 1 3 2 3 1 2 1
42 2 2 2 3 1 2 1 3 3 1 2 3 2
43 2 2 3 1 2 3 2 1 1 2 3 1 3
44 2 2 3 1 2 3 2 1 2 3 1 2 1
45 2 2 3 1 2 3 2 1 3 1 2 3 2
46 2 3 1 3 2 3 1 2 1 3 2 3 1
47 2 3 1 3 2 3 1 2 2 1 3 1 2
48 2 3 1 3 2 3 1 2 3 2 1 2 3
49 2 3 2 1 3 1 2 3 1 3 2 3 1
50 2 3 2 1 3 1 2 3 2 1 3 1 2
51 2 3 2 1 3 1 2 3 3 2 1 2 3
52 2 3 3 2 1 2 3 1 1 3 2 3 1
53 2 3 3 2 1 2 3 1 2 1 3 1 2
54 2 3 3 2 1 2 3 1 3 2 1 2 3
  14 15 16 17 18 19 20 21 22 23 24 25 26
1 1 1 1 1 1 1 1 1 1 1 1 1 1
2 2 2 2 2 2 2 2 2 2 2 2 2 2
3 3 3 3 3 3 3 3 3 3 3 3 3 3
42 1 2 3 2 3 2 3 2 3 2 3 2 3
5 2 3 1 3 1 3 1 3 1 3 1 3 1
6 3 1 2 1 2 1 2 1 2 1 2 1 2
7 1 3 2 3 2 3 2 3 2 3 2 3 2
8 2 1 3 1 3 1 3 1 3 1 3 1 3
9 3 2 1 2 1 2 1 2 1 2 1 2 1
10 3 1 1 1 1 2 3 2 3 2 3 2 3
11 1 2 2 2 2 3 1 3 1 1 3 1 3
12 2 3 3 3 3 1 2 1 2 2 1 2 1
13 3 2 3 2 3 3 2 3 2 1 1 1 1
14 1 3 1 3 1 1 3 1 3 2 2 2 2
15 2 1 2 1 2 2 1 2 1 3 3 3 3
16 3 3 2 3 2 1 1 1 1 2 3 2 3
17 1 1 3 1 3 2 2 2 2 3 1 3 1
18 2 2 1 2 1 3 3 3 3 1 2 1 2
19 3 1 1 2 3 1 1 3 2 2 3 3 2
20 1 2 2 3 1 2 2 1 3 3 1 1 3
21 2 3 3 1 2 3 3 2 1 1 2 2 1
22 3 2 3 3 2 2 3 1 1 3 2 1 1
23 1 3 1 1 3 3 1 2 2 1 3 2 2
24 2 1 2 2 1 1 2 3 3 2 1 3 3
25 3 3 2 1 1 3 2 2 3 1 1 2 3
26 1 1 3 2 2 1 3 3 1 2 2 3 1
27 2 2 1 3 3 2 1 1 2 3 3 1 2
28 1 1 1 3 2 3 2 2 3 2 3 1 1
29 2 2 2 1 3 1 3 3 1 3 1 2 2
30 3 3 3 2 1 2 1 1 2 1 2 3 3
31 1 2 3 1 1 1 1 3 2 3 2 2 3
32 2 3 1 2 2 2 2 1 3 1 3 3 1
33 3 1 2 3 3 3 3 2 1 2 1 1 2
34 1 3 2 2 3 2 3 1 1 1 1 3 2
35 2 1 3 3 1 3 1 2 2 2 2 1 3
36 3 2 1 1 2 1 2 3 3 3 3 2 1
37 2 1 1 2 3 3 2 1 1 3 2 2 3
38 3 2 2 3 1 1 3 2 2 1 3 3 1
39 1 3 3 1 2 2 1 3 3 2 1 1 2
40 2 2 3 3 2 1 1 2 3 1 1 3 2
41 3 3 1 1 3 2 2 3 1 2 2 1 3
42 1 1 2 2 1 3 3 1 2 3 3 2 1
43 2 3 2 1 1 2 3 3 2 2 3 1 1
44 3 1 3 2 2 3 1 1 3 3 1 2 2
45 1 2 1 3 3 1 2 2 1 1 2 3 3
46 2 1 1 3 2 2 3 3 2 1 1 2 3
47 3 2 2 1 3 3 1 1 3 2 2 3 1
48 1 3 3 2 1 1 2 2 1 3 3 1 2
49 2 2 3 1 1 3 2 1 1 2 3 3 2
50 3 3 1 2 2 1 3 2 2 3 1 1 3
51 1 1 2 3 3 2 1 3 3 1 2 2 1
52 2 3 2 2 3 1 1 2 3 3 2 1 1
53 3 1 3 3 1 2 2 3 1 1 3 2 2
54 1 2 1 1 2 3 3 1 2 2 1 3 3

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