Best Known (184−26, 184, s)-Nets in Base 3
(184−26, 184, 4547)-Net over F3 — Constructive and digital
Digital (158, 184, 4547)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (0, 13, 4)-net over F3, using
- net from sequence [i] based on digital (0, 3)-sequence over F3, using
- Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 0 and N(F) ≥ 4, using
- the rational function field F3(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 3)-sequence over F3, using
- digital (145, 171, 4543)-net over F3, using
- net defined by OOA [i] based on linear OOA(3171, 4543, F3, 26, 26) (dual of [(4543, 26), 117947, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(3171, 59059, F3, 26) (dual of [59059, 58888, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- linear OA(3171, 59049, F3, 26) (dual of [59049, 58878, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(3161, 59049, F3, 25) (dual of [59049, 58888, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(30, 10, F3, 0) (dual of [10, 10, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- OA 13-folding and stacking [i] based on linear OA(3171, 59059, F3, 26) (dual of [59059, 58888, 27]-code), using
- net defined by OOA [i] based on linear OOA(3171, 4543, F3, 26, 26) (dual of [(4543, 26), 117947, 27]-NRT-code), using
- digital (0, 13, 4)-net over F3, using
(184−26, 184, 28091)-Net over F3 — Digital
Digital (158, 184, 28091)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3184, 28091, F3, 2, 26) (dual of [(28091, 2), 55998, 27]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3184, 29551, F3, 2, 26) (dual of [(29551, 2), 58918, 27]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3182, 29550, F3, 2, 26) (dual of [(29550, 2), 58918, 27]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3182, 59100, F3, 26) (dual of [59100, 58918, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(19) [i] based on
- linear OA(3171, 59049, F3, 26) (dual of [59049, 58878, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(3131, 59049, F3, 20) (dual of [59049, 58918, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [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(25) ⊂ Ce(19) [i] based on
- OOA 2-folding [i] based on linear OA(3182, 59100, F3, 26) (dual of [59100, 58918, 27]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3182, 29550, F3, 2, 26) (dual of [(29550, 2), 58918, 27]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3184, 29551, F3, 2, 26) (dual of [(29551, 2), 58918, 27]-NRT-code), using
(184−26, 184, large)-Net in Base 3 — Upper bound on s
There is no (158, 184, large)-net in base 3, because
- 24 times m-reduction [i] would yield (158, 160, large)-net in base 3, but