Best Known (128, 128+22, s)-Nets in Base 8
(128, 128+22, 190678)-Net over F8 — Constructive and digital
Digital (128, 150, 190678)-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 (112, 134, 190650)-net over F8, using
- net defined by OOA [i] based on linear OOA(8134, 190650, F8, 22, 22) (dual of [(190650, 22), 4194166, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(8134, 2097150, F8, 22) (dual of [2097150, 2097016, 23]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(8134, 2097152, F8, 22) (dual of [2097152, 2097018, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(8134, 2097150, F8, 22) (dual of [2097150, 2097016, 23]-code), using
- net defined by OOA [i] based on linear OOA(8134, 190650, F8, 22, 22) (dual of [(190650, 22), 4194166, 23]-NRT-code), using
- digital (5, 16, 28)-net over F8, using
(128, 128+22, 381300)-Net in Base 8 — Constructive
(128, 150, 381300)-net in base 8, using
- net defined by OOA [i] based on OOA(8150, 381300, S8, 22, 22), using
- OA 11-folding and stacking [i] based on OA(8150, 4194300, S8, 22), using
- discarding factors 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
- discarding factors based on OA(8150, 4194310, S8, 22), using
- OA 11-folding and stacking [i] based on OA(8150, 4194300, S8, 22), using
(128, 128+22, 3499763)-Net over F8 — Digital
Digital (128, 150, 3499763)-net over F8, using
(128, 128+22, large)-Net in Base 8 — Upper bound on s
There is no (128, 150, large)-net in base 8, because
- 20 times m-reduction [i] would yield (128, 130, large)-net in base 8, but