Best Known (43, 67, s)-Nets in Base 8
(43, 67, 354)-Net over F8 — Constructive and digital
Digital (43, 67, 354)-net over F8, using
- 5 times m-reduction [i] based on digital (43, 72, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 36, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- trace code for nets [i] based on digital (7, 36, 177)-net over F64, using
(43, 67, 514)-Net in Base 8 — Constructive
(43, 67, 514)-net in base 8, using
- 1 times m-reduction [i] based on (43, 68, 514)-net in base 8, using
- base change [i] based on digital (26, 51, 514)-net over F16, using
- 1 times m-reduction [i] based on digital (26, 52, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 26, 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
- trace code for nets [i] based on digital (0, 26, 257)-net over F256, using
- 1 times m-reduction [i] based on digital (26, 52, 514)-net over F16, using
- base change [i] based on digital (26, 51, 514)-net over F16, using
(43, 67, 588)-Net over F8 — Digital
Digital (43, 67, 588)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(867, 588, F8, 24) (dual of [588, 521, 25]-code), using
- 73 step Varšamov–Edel lengthening with (ri) = (2, 5 times 0, 1, 23 times 0, 1, 42 times 0) [i] based on linear OA(863, 511, F8, 24) (dual of [511, 448, 25]-code), using
- the primitive narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- 73 step Varšamov–Edel lengthening with (ri) = (2, 5 times 0, 1, 23 times 0, 1, 42 times 0) [i] based on linear OA(863, 511, F8, 24) (dual of [511, 448, 25]-code), using
(43, 67, 83268)-Net in Base 8 — Upper bound on s
There is no (43, 67, 83269)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 3 214335 405420 625366 864857 764051 262918 675241 938156 491688 090664 > 867 [i]