Best Known (132, 132+22, s)-Nets in Base 3
(132, 132+22, 5376)-Net over F3 — Constructive and digital
Digital (132, 154, 5376)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (2, 13, 8)-net over F3, using
- net from sequence [i] based on digital (2, 7)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 2 and N(F) ≥ 8, using
- net from sequence [i] based on digital (2, 7)-sequence over F3, using
- digital (119, 141, 5368)-net over F3, using
- net defined by OOA [i] based on linear OOA(3141, 5368, F3, 22, 22) (dual of [(5368, 22), 117955, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(3141, 59048, F3, 22) (dual of [59048, 58907, 23]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(3141, 59049, F3, 22) (dual of [59049, 58908, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(3141, 59048, F3, 22) (dual of [59048, 58907, 23]-code), using
- net defined by OOA [i] based on linear OOA(3141, 5368, F3, 22, 22) (dual of [(5368, 22), 117955, 23]-NRT-code), using
- digital (2, 13, 8)-net over F3, using
(132, 132+22, 25993)-Net over F3 — Digital
Digital (132, 154, 25993)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3154, 25993, F3, 2, 22) (dual of [(25993, 2), 51832, 23]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3154, 29551, F3, 2, 22) (dual of [(29551, 2), 58948, 23]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] 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
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3152, 29550, F3, 2, 22) (dual of [(29550, 2), 58948, 23]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3154, 29551, F3, 2, 22) (dual of [(29551, 2), 58948, 23]-NRT-code), using
(132, 132+22, large)-Net in Base 3 — Upper bound on s
There is no (132, 154, large)-net in base 3, because
- 20 times m-reduction [i] would yield (132, 134, large)-net in base 3, but