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

15 × (1)

$P_{15}^1$ = 15

1 × (2)+13 × (1)

$P_{15}^2\times P_{13}^1$ = 1365

1 × (1)+3 × (1)+11 × (1)

$P_{15}^1\times P_{14}^1\times P_{13}^1$ = 2730

1 × (4)+11 × (1)

$P_{15}^4\times P_{11}^1$ = 15015

1 × (1)+5 × (1)+9 × (1)

$P_{15}^1\times P_{14}^1\times P_{13}^1$ = 2730

3 × (2)+9 × (1)

$P_{15}^2\times P_{13}^1$ = 1365

1 × (3)+3 × (1)+9 × (1)

$P_{15}^3\times P_{12}^1\times P_{11}^1$ = 60060

1 × (6)+9 × (1)

$P_{15}^6\times P_9^1$ = 45045

1 × (1)+7 × (2)

$P_{15}^1\times P_{14}^2$ = 1365

3 × (1)+5 × (1)+7 × (1)

$P_{15}^1\times P_{14}^1\times P_{13}^1$ = 2730

1 × (3)+5 × (1)+7 × (1)

$P_{15}^3\times P_{12}^1\times P_{11}^1$ = 60060

1 × (2)+3 × (2)+7 × (1)

$P_{15}^2\times P_{13}^2\times P_{11}^1$ = 90090

1 × (5)+3 × (1)+7 × (1)

$P_{15}^5\times P_{10}^1\times P_9^1$ = 270270

1 × (8)+7 × (1)

$P_{15}^8\times P_7^1$ = 450450

5 × (3)

$P_{15}^3$ = 455

1 × (2)+3 × (1)+5 × (2)

$P_{15}^2\times P_{13}^1\times P_{12}^2$ = 90090

1 × (5)+5 × (2)

$P_{15}^5\times P_{10}^2$ = 135135

1 × (1)+3 × (3)+5 × (1)

$P_{15}^1\times P_{14}^3\times P_{11}^1$ = 60060

1 × 4+3 × 2+5 × 1

$P_{15}^4\times P_{11}^2\times P_9^1$ = 675675

1 × (7)+3 × (1)+5 × (1)

$P_{15}^7\times P_8^1\times P_7^1$ = 360360

1 × (10)+5 × (1)

$P_{15}^{10}\times P_5^1$ = 15015

3 × (5)

$P_{15}^5$ = 3003

1 × (3)+3 × (4)

$P_{15}^3\times P_{12}^4$ = 225225

1 × (6)+3 × (3)

$P_{15}^6\times P_9^3$ = 420420

1 × (9)+3 × (2)

$P_{15}^9\times P_6^2$ = 75075

1 × (12)+3 × (1)

$P_{15}^{12}\times P_3^1$ = 1365

1 × (15)

$P_{15}^{15}$ = 1

Possible weighted

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