# Table 7 Weight combinations, permutations and possible weights sum values in the restricted grid search scheme

Weight combinations*

Number of corresponding weight**

15 Ã— (1)

${P}_{15}^{1}$ = 15

1 Ã— (2)+13 Ã— (1)

${P}_{15}^{2}Ã—{P}_{13}^{1}$ = 1365

1 Ã— (1)+3 Ã— (1)+11 Ã— (1)

${P}_{15}^{1}Ã—{P}_{14}^{1}Ã—{P}_{13}^{1}$ = 2730

1 Ã— (4)+11 Ã— (1)

${P}_{15}^{4}Ã—{P}_{11}^{1}$ = 15015

1 Ã— (1)+5 Ã— (1)+9 Ã— (1)

${P}_{15}^{1}Ã—{P}_{14}^{1}Ã—{P}_{13}^{1}$ = 2730

3 Ã— (2)+9 Ã— (1)

${P}_{15}^{2}Ã—{P}_{13}^{1}$ = 1365

1 Ã— (3)+3 Ã— (1)+9 Ã— (1)

${P}_{15}^{3}Ã—{P}_{12}^{1}Ã—{P}_{11}^{1}$ = 60060

1 Ã— (6)+9 Ã— (1)

${P}_{15}^{6}Ã—{P}_{9}^{1}$ = 45045

1 Ã— (1)+7 Ã— (2)

${P}_{15}^{1}Ã—{P}_{14}^{2}$ = 1365

3 Ã— (1)+5 Ã— (1)+7 Ã— (1)

${P}_{15}^{1}Ã—{P}_{14}^{1}Ã—{P}_{13}^{1}$ = 2730

1 Ã— (3)+5 Ã— (1)+7 Ã— (1)

${P}_{15}^{3}Ã—{P}_{12}^{1}Ã—{P}_{11}^{1}$ = 60060

1 Ã— (2)+3 Ã— (2)+7 Ã— (1)

${P}_{15}^{2}Ã—{P}_{13}^{2}Ã—{P}_{11}^{1}$ = 90090

1 Ã— (5)+3 Ã— (1)+7 Ã— (1)

${P}_{15}^{5}Ã—{P}_{10}^{1}Ã—{P}_{9}^{1}$ = 270270

1 Ã— (8)+7 Ã— (1)

${P}_{15}^{8}Ã—{P}_{7}^{1}$ = 450450

5 Ã— (3)

${P}_{15}^{3}$ = 455

1 Ã— (2)+3 Ã— (1)+5 Ã— (2)

${P}_{15}^{2}Ã—{P}_{13}^{1}Ã—{P}_{12}^{2}$ = 90090

1 Ã— (5)+5 Ã— (2)

${P}_{15}^{5}Ã—{P}_{10}^{2}$ = 135135

1 Ã— (1)+3 Ã— (3)+5 Ã— (1)

${P}_{15}^{1}Ã—{P}_{14}^{3}Ã—{P}_{11}^{1}$ = 60060

1 Ã— 4+3 Ã— 2+5 Ã— 1

${P}_{15}^{4}Ã—{P}_{11}^{2}Ã—{P}_{9}^{1}$ = 675675

1 Ã— (7)+3 Ã— (1)+5 Ã— (1)

${P}_{15}^{7}Ã—{P}_{8}^{1}Ã—{P}_{7}^{1}$ = 360360

1 Ã— (10)+5 Ã— (1)

${P}_{15}^{10}Ã—{P}_{5}^{1}$ = 15015

3 Ã— (5)

${P}_{15}^{5}$ = 3003

1 Ã— (3)+3 Ã— (4)

${P}_{15}^{3}Ã—{P}_{12}^{4}$ = 225225

1 Ã— (6)+3 Ã— (3)

${P}_{15}^{6}Ã—{P}_{9}^{3}$ = 420420

1 Ã— (9)+3 Ã— (2)

${P}_{15}^{9}Ã—{P}_{6}^{2}$ = 75075

1 Ã— (12)+3 Ã— (1)

${P}_{15}^{12}Ã—{P}_{3}^{1}$ = 1365

1 Ã— (15)

${P}_{15}^{15}$ = 1

Possible weighted

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15

1. * Weight combinations are denoted as the sum of each weight value multiplied by the number of weights taking the weight value, with the weight value = 0 omitted.
2. ** For instance, "15 Ã— (1)"represents that 1 of the 15 weights takes the value 15, and the other 14 weights take the value 0; and "1 Ã— (1)+3 Ã— (1)+11 Ã— (1)" represents that 1 of the 15 weights takes the value 1, 1 weight takes the value 3, 1 weight takes 11 and the remaining 12 weights take the value 0. Each weight combination corresponds to one or more weight permutations. For instance, for weight combination "15 Ã— (1)," the weight value 15 can be taken by each of the 15 weights; thus, it corresponds to ${P}_{15}^{1}$ weight permutations.