Best Known (151−22, 151, s)-Nets in Base 8
(151−22, 151, 190679)-Net over F8 — Constructive and digital
Digital (129, 151, 190679)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (5, 16, 28)-net over F8, using
- net from sequence [i] based on digital (5, 27)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 5 and N(F) ≥ 28, using
- net from sequence [i] based on digital (5, 27)-sequence over F8, using
- digital (113, 135, 190651)-net over F8, using
- net defined by OOA [i] based on linear OOA(8135, 190651, F8, 22, 22) (dual of [(190651, 22), 4194187, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(8135, 2097161, F8, 22) (dual of [2097161, 2097026, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(8135, 2097167, F8, 22) (dual of [2097167, 2097032, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(19) [i] based on
- linear OA(8134, 2097152, F8, 22) (dual of [2097152, 2097018, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(8120, 2097152, F8, 20) (dual of [2097152, 2097032, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(81, 15, F8, 1) (dual of [15, 14, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(21) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(8135, 2097167, F8, 22) (dual of [2097167, 2097032, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(8135, 2097161, F8, 22) (dual of [2097161, 2097026, 23]-code), using
- net defined by OOA [i] based on linear OOA(8135, 190651, F8, 22, 22) (dual of [(190651, 22), 4194187, 23]-NRT-code), using
- digital (5, 16, 28)-net over F8, using
(151−22, 151, 381301)-Net in Base 8 — Constructive
(129, 151, 381301)-net in base 8, using
- net defined by OOA [i] based on OOA(8151, 381301, S8, 22, 22), using
- OA 11-folding and stacking [i] based on OA(8151, 4194311, S8, 22), using
- 1 times code embedding in larger space [i] based on OA(8150, 4194310, S8, 22), using
- trace code [i] based on OA(6475, 2097155, S64, 22), using
- discarding parts of the base [i] based on linear OA(12864, 2097155, F128, 22) (dual of [2097155, 2097091, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- linear OA(12864, 2097152, F128, 22) (dual of [2097152, 2097088, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(12861, 2097152, F128, 21) (dual of [2097152, 2097091, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(1280, 3, F128, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- discarding parts of the base [i] based on linear OA(12864, 2097155, F128, 22) (dual of [2097155, 2097091, 23]-code), using
- trace code [i] based on OA(6475, 2097155, S64, 22), using
- 1 times code embedding in larger space [i] based on OA(8150, 4194310, S8, 22), using
- OA 11-folding and stacking [i] based on OA(8151, 4194311, S8, 22), using
(151−22, 151, 3864050)-Net over F8 — Digital
Digital (129, 151, 3864050)-net over F8, using
(151−22, 151, large)-Net in Base 8 — Upper bound on s
There is no (129, 151, large)-net in base 8, because
- 20 times m-reduction [i] would yield (129, 131, large)-net in base 8, but