Best Known (120−23, 120, s)-Nets in Base 8
(120−23, 120, 3014)-Net over F8 — Constructive and digital
Digital (97, 120, 3014)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (8, 19, 35)-net over F8, using
- net from sequence [i] based on digital (8, 34)-sequence over F8, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F8 with g(F) = 7, N(F) = 34, and 1 place with degree 2 [i] based on function field F/F8 with g(F) = 7 and N(F) ≥ 34, using a function field by Sémirat [i]
- net from sequence [i] based on digital (8, 34)-sequence over F8, using
- digital (78, 101, 2979)-net over F8, using
- net defined by OOA [i] based on linear OOA(8101, 2979, F8, 23, 23) (dual of [(2979, 23), 68416, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(8101, 32770, F8, 23) (dual of [32770, 32669, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(8101, 32773, F8, 23) (dual of [32773, 32672, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(21) [i] based on
- linear OA(8101, 32768, F8, 23) (dual of [32768, 32667, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(896, 32768, F8, 22) (dual of [32768, 32672, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(80, 5, F8, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(22) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(8101, 32773, F8, 23) (dual of [32773, 32672, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(8101, 32770, F8, 23) (dual of [32770, 32669, 24]-code), using
- net defined by OOA [i] based on linear OOA(8101, 2979, F8, 23, 23) (dual of [(2979, 23), 68416, 24]-NRT-code), using
- digital (8, 19, 35)-net over F8, using
(120−23, 120, 11915)-Net in Base 8 — Constructive
(97, 120, 11915)-net in base 8, using
- base change [i] based on digital (67, 90, 11915)-net over F16, using
- net defined by OOA [i] based on linear OOA(1690, 11915, F16, 23, 23) (dual of [(11915, 23), 273955, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(1690, 131066, F16, 23) (dual of [131066, 130976, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(1690, 131074, F16, 23) (dual of [131074, 130984, 24]-code), using
- trace code [i] based on linear OA(25645, 65537, F256, 23) (dual of [65537, 65492, 24]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- trace code [i] based on linear OA(25645, 65537, F256, 23) (dual of [65537, 65492, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(1690, 131074, F16, 23) (dual of [131074, 130984, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(1690, 131066, F16, 23) (dual of [131066, 130976, 24]-code), using
- net defined by OOA [i] based on linear OOA(1690, 11915, F16, 23, 23) (dual of [(11915, 23), 273955, 24]-NRT-code), using
(120−23, 120, 109080)-Net over F8 — Digital
Digital (97, 120, 109080)-net over F8, using
(120−23, 120, large)-Net in Base 8 — Upper bound on s
There is no (97, 120, large)-net in base 8, because
- 21 times m-reduction [i] would yield (97, 99, large)-net in base 8, but