Best Known (29, 46, s)-Nets in Base 128
(29, 46, 2327)-Net over F128 — Constructive and digital
Digital (29, 46, 2327)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (5, 13, 279)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (0, 4, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 0 and N(F) ≥ 129, using
- the rational function field F128(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- digital (1, 9, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- digital (0, 4, 129)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (16, 33, 2048)-net over F128, using
- net defined by OOA [i] based on linear OOA(12833, 2048, F128, 17, 17) (dual of [(2048, 17), 34783, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(12833, 16385, F128, 17) (dual of [16385, 16352, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- OOA 8-folding and stacking with additional row [i] based on linear OA(12833, 16385, F128, 17) (dual of [16385, 16352, 18]-code), using
- net defined by OOA [i] based on linear OOA(12833, 2048, F128, 17, 17) (dual of [(2048, 17), 34783, 18]-NRT-code), using
- digital (5, 13, 279)-net over F128, using
(29, 46, 8321)-Net in Base 128 — Constructive
(29, 46, 8321)-net in base 128, using
- (u, u+v)-construction [i] based on
- digital (0, 8, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 0 and N(F) ≥ 129, using
- the rational function field F128(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- (21, 38, 8192)-net in base 128, using
- net defined by OOA [i] based on OOA(12838, 8192, S128, 17, 17), using
- OOA 8-folding and stacking with additional row [i] based on OA(12838, 65537, S128, 17), using
- discarding factors based on OA(12838, 65538, S128, 17), using
- discarding parts of the base [i] based on linear OA(25633, 65538, F256, 17) (dual of [65538, 65505, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- linear OA(25633, 65536, F256, 17) (dual of [65536, 65503, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(25631, 65536, F256, 16) (dual of [65536, 65505, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(2560, 2, F256, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(2560, s, F256, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- discarding parts of the base [i] based on linear OA(25633, 65538, F256, 17) (dual of [65538, 65505, 18]-code), using
- discarding factors based on OA(12838, 65538, S128, 17), using
- OOA 8-folding and stacking with additional row [i] based on OA(12838, 65537, S128, 17), using
- net defined by OOA [i] based on OOA(12838, 8192, S128, 17, 17), using
- digital (0, 8, 129)-net over F128, using
(29, 46, 61238)-Net over F128 — Digital
Digital (29, 46, 61238)-net over F128, using
(29, 46, large)-Net in Base 128 — Upper bound on s
There is no (29, 46, large)-net in base 128, because
- 15 times m-reduction [i] would yield (29, 31, large)-net in base 128, but