Best Known (33, 33+18, s)-Nets in Base 128
(33, 33+18, 2207)-Net over F128 — Constructive and digital
Digital (33, 51, 2207)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (7, 16, 387)-net over F128, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 3, 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 (0, 4, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128 (see above)
- digital (0, 9, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128 (see above)
- digital (0, 3, 129)-net over F128, using
- generalized (u, u+v)-construction [i] based on
- digital (17, 35, 1820)-net over F128, using
- net defined by OOA [i] based on linear OOA(12835, 1820, F128, 18, 18) (dual of [(1820, 18), 32725, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(12835, 16380, F128, 18) (dual of [16380, 16345, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(12835, 16384, F128, 18) (dual of [16384, 16349, 19]-code), using
- an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- discarding factors / shortening the dual code based on linear OA(12835, 16384, F128, 18) (dual of [16384, 16349, 19]-code), using
- OA 9-folding and stacking [i] based on linear OA(12835, 16380, F128, 18) (dual of [16380, 16345, 19]-code), using
- net defined by OOA [i] based on linear OOA(12835, 1820, F128, 18, 18) (dual of [(1820, 18), 32725, 19]-NRT-code), using
- digital (7, 16, 387)-net over F128, using
(33, 33+18, 7539)-Net in Base 128 — Constructive
(33, 51, 7539)-net in base 128, using
- (u, u+v)-construction [i] based on
- (2, 11, 257)-net in base 128, using
- 5 times m-reduction [i] based on (2, 16, 257)-net in base 128, using
- base change [i] based on digital (0, 14, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- base change [i] based on digital (0, 14, 257)-net over F256, using
- 5 times m-reduction [i] based on (2, 16, 257)-net in base 128, using
- (22, 40, 7282)-net in base 128, using
- base change [i] based on digital (17, 35, 7282)-net over F256, using
- net defined by OOA [i] based on linear OOA(25635, 7282, F256, 18, 18) (dual of [(7282, 18), 131041, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(25635, 65538, F256, 18) (dual of [65538, 65503, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(16) [i] based on
- linear OA(25635, 65536, F256, 18) (dual of [65536, 65501, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- 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(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(17) ⊂ Ce(16) [i] based on
- OA 9-folding and stacking [i] based on linear OA(25635, 65538, F256, 18) (dual of [65538, 65503, 19]-code), using
- net defined by OOA [i] based on linear OOA(25635, 7282, F256, 18, 18) (dual of [(7282, 18), 131041, 19]-NRT-code), using
- base change [i] based on digital (17, 35, 7282)-net over F256, using
- (2, 11, 257)-net in base 128, using
(33, 33+18, 118523)-Net over F128 — Digital
Digital (33, 51, 118523)-net over F128, using
(33, 33+18, large)-Net in Base 128 — Upper bound on s
There is no (33, 51, large)-net in base 128, because
- 16 times m-reduction [i] would yield (33, 35, large)-net in base 128, but