Best Known (66−24, 66, s)-Nets in Base 128
(66−24, 66, 1644)-Net over F128 — Constructive and digital
Digital (42, 66, 1644)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (7, 19, 279)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (0, 6, 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, 13, 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, 6, 129)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (23, 47, 1365)-net over F128, using
- net defined by OOA [i] based on linear OOA(12847, 1365, F128, 24, 24) (dual of [(1365, 24), 32713, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(12847, 16380, F128, 24) (dual of [16380, 16333, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(12847, 16384, F128, 24) (dual of [16384, 16337, 25]-code), using
- an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- discarding factors / shortening the dual code based on linear OA(12847, 16384, F128, 24) (dual of [16384, 16337, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(12847, 16380, F128, 24) (dual of [16380, 16333, 25]-code), using
- net defined by OOA [i] based on linear OOA(12847, 1365, F128, 24, 24) (dual of [(1365, 24), 32713, 25]-NRT-code), using
- digital (7, 19, 279)-net over F128, using
(66−24, 66, 5590)-Net in Base 128 — Constructive
(42, 66, 5590)-net in base 128, using
- (u, u+v)-construction [i] based on
- digital (0, 12, 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
- (30, 54, 5461)-net in base 128, using
- net defined by OOA [i] based on OOA(12854, 5461, S128, 24, 24), using
- OA 12-folding and stacking [i] based on OA(12854, 65532, S128, 24), using
- discarding factors based on OA(12854, 65538, S128, 24), using
- discarding parts of the base [i] based on linear OA(25647, 65538, F256, 24) (dual of [65538, 65491, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(22) [i] based on
- linear OA(25647, 65536, F256, 24) (dual of [65536, 65489, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(25645, 65536, F256, 23) (dual of [65536, 65491, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [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(23) ⊂ Ce(22) [i] based on
- discarding parts of the base [i] based on linear OA(25647, 65538, F256, 24) (dual of [65538, 65491, 25]-code), using
- discarding factors based on OA(12854, 65538, S128, 24), using
- OA 12-folding and stacking [i] based on OA(12854, 65532, S128, 24), using
- net defined by OOA [i] based on OOA(12854, 5461, S128, 24, 24), using
- digital (0, 12, 129)-net over F128, using
(66−24, 66, 82697)-Net over F128 — Digital
Digital (42, 66, 82697)-net over F128, using
(66−24, 66, large)-Net in Base 128 — Upper bound on s
There is no (42, 66, large)-net in base 128, because
- 22 times m-reduction [i] would yield (42, 44, large)-net in base 128, but