Net Designs

Digital Net Designs and Orthogonal Arrays

Each design comes from a digital net and has n = 2^m runs and levels. By collapseing the levels, one may obtain both single level and mixed level orthogonal arrays.

16-run, 15-factor by computer search
16-run, 15-factor by low discrepancy point sets
32-run, 15-factor by computer search
64-run, 15-factor by computer search
16/64-run, 15-factor by computer search

Columns of the tables correspond to strength of the designs.
Rows of the tables correspond to number of levels per factor after collapse.
The numbers in the first row are the strengths of the design.
The numbers in the first column are the number of levels per factor after collapse.
The numbers in the elements of the tables are the numbers of factors that have the corresponding strengths when the arrays are collapsed to corresponding levels.
The blue elements have the same strengths as the designs in Sloane's table (which also attain Rao's upper bound).
The green elements meet Rao's upper bound.
'×' means that is impossible to have this strength given the number of rows.

Click on the design names for the arrays with different settings.

16-run, 15-factor designs by computer search

Design 1
	2	3	4
2¹⁵	15	-	5
4 × 2¹⁴	13	3	×
4² × 2¹³	11	×	×
4³ × 2¹²	9	×	×
4⁴ × 2¹¹	7	×	×
4¹⁵	5	×	×
8 × 2¹⁴	6	×	×

Design 2
	2	3	4
2¹⁵	15	-	4
4 × 2¹⁴	13	4	×
4² × 2¹³	11	×	×
4³ × 2¹²	9	×	×
4⁴ × 2¹¹	7	×	×
4¹⁵	5	×	×
8 × 2¹⁴	3	×	×

Design 3
	2	3	4
2¹⁵	15	-	5
4 × 2¹⁴	13	3	×
4² × 2¹³	8	×	×
4³ × 2¹²	7	×	×
4¹⁵	5	×	×
8 × 2¹⁴	9	×	×

Design 4
	2	3	4
2¹⁵	15	5	4
4 × 2¹⁴	13	4	×
4² × 2¹³	11	×	×
4³ × 2¹²	9	×	×
4¹⁵	4	×	×
8 × 2¹⁴	3	×	×

Design 5
	2	3	4
2¹⁵	15	6	4
4 × 2¹⁴	13	4	×
4² × 2¹³	11	×	×
4³ × 2¹²	5	×	×
4¹⁵	4	×	×
8 × 2¹⁴	3	×	×

Design 6
	2	3	4
2¹⁵	15	7	4
4 × 2¹⁴	13	4	×
4² × 2¹³	6	×	×
4³ × 2¹²	5	×	×
4¹⁵	4	×	×
8 × 2¹⁴	3	×	×

Design 7
	2	3	4
2¹⁵	15	8	4
4 × 2¹⁴	7	4	×
4² × 2¹³	6	×	×
4³ × 2¹²	5	×	×
4¹⁵	4	×	×
8 × 2¹⁴	3	×	×

Design 8
	2	3	4
2¹⁵	15	-	5
4 × 2¹⁴	-	4	×
4¹⁵	4	×	×
8 × 2¹⁴	3	×	×

16-run, 15-factor by low-discrepancy point sets

Sobol Point Set Design
	2	3	4
2¹⁵	7	-	4
4 × 2¹⁴	7	3	×
4² × 2¹³	6	×	×
4¹⁵	5	×	×
8 × 2¹⁴	7	×	×

Niederreiter Point Set Design
	2	3	4
2¹⁵	5	-	4
4 × 2¹⁴	5	3	×
4⁴ × 2¹¹	5	×	×
4¹⁵	4	×	×
8 × 2¹⁴	5	×	×

32-run, 15-factor designs by computer search

Design 1
	2	3	4	5
2¹⁵	-	15	-	6
4 × 2¹⁴	15	5	4	×
4² × 2¹³	14	5	×	×
4³ × 2¹²	13	×	×	×
4⁴ × 2¹¹	12	×	×	×
4⁵ × 2¹⁰	11	×	×	×
4⁶ × 2⁹	10	×	×	×
4¹⁵	8	×	×	×
8 × 2¹⁴	11	4	×	×

Design 2
	2	3	4	5
2¹⁵	15	9	-	5
4 × 2¹⁴	15	8	4	×
4² × 2¹³	8	6	×	×
4³ × 2¹²	8	×	×	×
4¹⁵	7	×	×	×
8 × 2¹⁴	5	3	×	×
8 × 4 × 2¹³	5	×	×	×

Design 3
	2	3	4	5
2¹⁵	15	8	-	6
4² × 2¹³	-	5	×	×
4⁸ × 2⁷	15	×	×	×
4¹⁵	9	×	×	×
8 × 4³ × 2¹¹	15	×	×	×
16 × 2¹⁴	3	×	×	×

64-run, 15-factor designs by computer search

Design 1
	2	3	4	5	6
2¹⁵	-	15	-	-	7
4 × 2¹⁴	15	-	6	5	×
4² × 2¹³	15	6	5	×	×
4³ × 2¹²	15	6	×	×	×
4¹⁵	15	4	×	×	×
8 × 2¹⁴	15	6	4	×	×
8² × 2¹³	14	×	×	×	×
8⁴ × 2¹¹	13	×	×	×	×
8¹⁵	6	×	×	×	×
8 × 4 × 2¹³	15	3	×	×	×
8 × 4⁶ × 2⁸	15	×	×	×	×

Design 2
	2	3	4	5	6
2¹⁵	-	15	-	-	7
4 × 2¹⁴	15	-	6	5	×
4² × 2¹³	15	6	5	×	×
4³ × 2¹²	15	6	×	×	×
4¹⁵	15	4	×	×	×
8 × 2¹⁴	15	-	4	×	×
8⁵ × 2¹⁰	15	×	×	×	×
8⁶ × 2⁹	13	×	×	×	×
8⁷ × 2⁸	12	×	×	×	×
8⁸ × 2⁷	11	×	×	×	×
8¹⁵	9	×	×	×	×
8 × 4¹⁴	14	×	×	×	×
8² × 4¹³	12	×	×	×	×
8³ × 4¹²	11	×	×	×	×
8⁴ × 4¹¹	10	×	×	×	×
8 × 4¹³× 2	15	×	×	×	×
8⁶ × 4²× 2⁷	13	×	×	×	×

Design 3
	2	3	4	5	6
2¹⁵	-	15	-	-	6
4 × 2¹⁴	-	15	-	6	×
4² × 2¹³	15	12	4	×	×
4³ × 2¹²	15	10	×	×	×
4¹⁵	15	6	×	×	×
8 × 2¹⁴	9	-	-	×	×
8³ × 2¹²	8	×	×	×	×
8¹⁵	4	×	×	×	×
8 × 4¹⁴	5	×	×	×	×

Design 4
	2	3	4	5	6
2¹⁵	15	9	-	-	7
4 × 2¹⁴	-	-	-	6	×
4² × 2¹³	6	-	5	×	×
4³ × 2¹²	6	5	×	×	×
4¹⁵	6	4	×	×	×
8 × 2¹⁴	6	5	4	×	×
8¹⁵	6	×	×	×	×

16/64-run, 15-factor designs by computer search

Design 1
64-run	2	3	4	5	6
2¹⁵	-	15	-	-	7
4 × 2¹⁴	15	-	6	5	×
4² × 2¹³	15	-	4	×	×
4¹⁵	15	4	×	×	×
8³ × 2¹²	14	×	×	×	×
8⁴ × 2¹¹	13	×	×	×	×
8⁵ × 2¹⁰	9	×	×	×	×
8¹⁵	6	×	×	×	×
16-run	2	3	4	5	6
2¹⁵	6	-	5	×	×
4 × 2¹⁴	6	3	×	×	×
8 × 2¹⁴	6	×	×	×	×
4¹⁵	5	×	×	×	×