Best Known (130−22, 130, s)-Nets in Base 9
(130−22, 130, 96626)-Net over F9 — Constructive and digital
Digital (108, 130, 96626)-net over F9, using
- 92 times duplication [i] based on digital (106, 128, 96626)-net over F9, using
- net defined by OOA [i] based on linear OOA(9128, 96626, F9, 22, 22) (dual of [(96626, 22), 2125644, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(9128, 1062886, F9, 22) (dual of [1062886, 1062758, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(9128, 1062888, F9, 22) (dual of [1062888, 1062760, 23]-code), using
- trace code [i] based on linear OA(8164, 531444, F81, 22) (dual of [531444, 531380, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- linear OA(8164, 531441, F81, 22) (dual of [531441, 531377, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(8161, 531441, F81, 21) (dual of [531441, 531380, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(810, 3, F81, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(810, s, F81, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- trace code [i] based on linear OA(8164, 531444, F81, 22) (dual of [531444, 531380, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(9128, 1062888, F9, 22) (dual of [1062888, 1062760, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(9128, 1062886, F9, 22) (dual of [1062886, 1062758, 23]-code), using
- net defined by OOA [i] based on linear OOA(9128, 96626, F9, 22, 22) (dual of [(96626, 22), 2125644, 23]-NRT-code), using
(130−22, 130, 1062896)-Net over F9 — Digital
Digital (108, 130, 1062896)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9130, 1062896, F9, 22) (dual of [1062896, 1062766, 23]-code), using
- trace code [i] based on linear OA(8165, 531448, F81, 22) (dual of [531448, 531383, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(19) [i] based on
- linear OA(8164, 531441, F81, 22) (dual of [531441, 531377, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(8158, 531441, F81, 20) (dual of [531441, 531383, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(811, 7, F81, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(811, s, F81, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(21) ⊂ Ce(19) [i] based on
- trace code [i] based on linear OA(8165, 531448, F81, 22) (dual of [531448, 531383, 23]-code), using
(130−22, 130, large)-Net in Base 9 — Upper bound on s
There is no (108, 130, large)-net in base 9, because
- 20 times m-reduction [i] would yield (108, 110, large)-net in base 9, but