Best Known (120−22, 120, s)-Nets in Base 9
(120−22, 120, 48315)-Net over F9 — Constructive and digital
Digital (98, 120, 48315)-net over F9, using
- net defined by OOA [i] based on linear OOA(9120, 48315, F9, 22, 22) (dual of [(48315, 22), 1062810, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(9120, 531465, F9, 22) (dual of [531465, 531345, 23]-code), using
- construction XX applied to Ce(21) ⊂ Ce(18) ⊂ Ce(16) [i] based on
- linear OA(9115, 531441, F9, 22) (dual of [531441, 531326, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(997, 531441, F9, 19) (dual of [531441, 531344, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(991, 531441, F9, 17) (dual of [531441, 531350, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(93, 22, F9, 2) (dual of [22, 19, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(93, 80, F9, 2) (dual of [80, 77, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(93, 80, F9, 2) (dual of [80, 77, 3]-code), using
- linear OA(91, 2, F9, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
- construction XX applied to Ce(21) ⊂ Ce(18) ⊂ Ce(16) [i] based on
- OA 11-folding and stacking [i] based on linear OA(9120, 531465, F9, 22) (dual of [531465, 531345, 23]-code), using
(120−22, 120, 494253)-Net over F9 — Digital
Digital (98, 120, 494253)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9120, 494253, F9, 22) (dual of [494253, 494133, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(9120, 531465, F9, 22) (dual of [531465, 531345, 23]-code), using
- construction XX applied to Ce(21) ⊂ Ce(18) ⊂ Ce(16) [i] based on
- linear OA(9115, 531441, F9, 22) (dual of [531441, 531326, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(997, 531441, F9, 19) (dual of [531441, 531344, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(991, 531441, F9, 17) (dual of [531441, 531350, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 531440 = 96−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(93, 22, F9, 2) (dual of [22, 19, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(93, 80, F9, 2) (dual of [80, 77, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(93, 80, F9, 2) (dual of [80, 77, 3]-code), using
- linear OA(91, 2, F9, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
- construction XX applied to Ce(21) ⊂ Ce(18) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(9120, 531465, F9, 22) (dual of [531465, 531345, 23]-code), using
(120−22, 120, large)-Net in Base 9 — Upper bound on s
There is no (98, 120, large)-net in base 9, because
- 20 times m-reduction [i] would yield (98, 100, large)-net in base 9, but