Best Known (130, 152, s)-Nets in Base 3
(130, 152, 5372)-Net over F3 — Constructive and digital
Digital (130, 152, 5372)-net over F3, using
- net defined by OOA [i] based on linear OOA(3152, 5372, F3, 22, 22) (dual of [(5372, 22), 118032, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(3152, 59092, F3, 22) (dual of [59092, 58940, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(3152, 59100, F3, 22) (dual of [59100, 58948, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(15) [i] based on
- linear OA(3141, 59049, F3, 22) (dual of [59049, 58908, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(3101, 59049, F3, 16) (dual of [59049, 58948, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(311, 51, F3, 5) (dual of [51, 40, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(311, 85, F3, 5) (dual of [85, 74, 6]-code), using
- construction X applied to Ce(21) ⊂ Ce(15) [i] based on
- discarding factors / shortening the dual code based on linear OA(3152, 59100, F3, 22) (dual of [59100, 58948, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(3152, 59092, F3, 22) (dual of [59092, 58940, 23]-code), using
(130, 152, 23152)-Net over F3 — Digital
Digital (130, 152, 23152)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3152, 23152, F3, 2, 22) (dual of [(23152, 2), 46152, 23]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3152, 29550, F3, 2, 22) (dual of [(29550, 2), 58948, 23]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3152, 59100, F3, 22) (dual of [59100, 58948, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(15) [i] based on
- linear OA(3141, 59049, F3, 22) (dual of [59049, 58908, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(3101, 59049, F3, 16) (dual of [59049, 58948, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(311, 51, F3, 5) (dual of [51, 40, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(311, 85, F3, 5) (dual of [85, 74, 6]-code), using
- construction X applied to Ce(21) ⊂ Ce(15) [i] based on
- OOA 2-folding [i] based on linear OA(3152, 59100, F3, 22) (dual of [59100, 58948, 23]-code), using
- discarding factors / shortening the dual code based on linear OOA(3152, 29550, F3, 2, 22) (dual of [(29550, 2), 58948, 23]-NRT-code), using
(130, 152, large)-Net in Base 3 — Upper bound on s
There is no (130, 152, large)-net in base 3, because
- 20 times m-reduction [i] would yield (130, 132, large)-net in base 3, but