Best Known (130, 130+21, s)-Nets in Base 3
(130, 130+21, 5911)-Net over F3 — Constructive and digital
Digital (130, 151, 5911)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (1, 11, 7)-net over F3, using
- net from sequence [i] based on digital (1, 6)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 1 and N(F) ≥ 7, using
- net from sequence [i] based on digital (1, 6)-sequence over F3, using
- digital (119, 140, 5904)-net over F3, using
- net defined by OOA [i] based on linear OOA(3140, 5904, F3, 21, 21) (dual of [(5904, 21), 123844, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(3140, 59041, F3, 21) (dual of [59041, 58901, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(3140, 59048, F3, 21) (dual of [59048, 58908, 22]-code), using
- 1 times truncation [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]
- 1 times truncation [i] based on linear OA(3141, 59049, F3, 22) (dual of [59049, 58908, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(3140, 59048, F3, 21) (dual of [59048, 58908, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(3140, 59041, F3, 21) (dual of [59041, 58901, 22]-code), using
- net defined by OOA [i] based on linear OOA(3140, 5904, F3, 21, 21) (dual of [(5904, 21), 123844, 22]-NRT-code), using
- digital (1, 11, 7)-net over F3, using
(130, 130+21, 29549)-Net over F3 — Digital
Digital (130, 151, 29549)-net over F3, using
- 31 times duplication [i] based on digital (129, 150, 29549)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3150, 29549, F3, 2, 21) (dual of [(29549, 2), 58948, 22]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3150, 59098, F3, 21) (dual of [59098, 58948, 22]-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(39, 49, F3, 4) (dual of [49, 40, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(39, 80, F3, 4) (dual of [80, 71, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(39, 80, F3, 4) (dual of [80, 71, 5]-code), using
- construction X applied to Ce(21) ⊂ Ce(15) [i] based on
- OOA 2-folding [i] based on linear OA(3150, 59098, F3, 21) (dual of [59098, 58948, 22]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3150, 29549, F3, 2, 21) (dual of [(29549, 2), 58948, 22]-NRT-code), using
(130, 130+21, large)-Net in Base 3 — Upper bound on s
There is no (130, 151, large)-net in base 3, because
- 19 times m-reduction [i] would yield (130, 132, large)-net in base 3, but