Best Known (19, 29, s)-Nets in Base 8
(19, 29, 208)-Net over F8 — Constructive and digital
Digital (19, 29, 208)-net over F8, using
- 3 times m-reduction [i] based on digital (19, 32, 208)-net over F8, using
- trace code for nets [i] based on digital (3, 16, 104)-net over F64, using
- net from sequence [i] based on digital (3, 103)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 3 and N(F) ≥ 104, using
- net from sequence [i] based on digital (3, 103)-sequence over F64, using
- trace code for nets [i] based on digital (3, 16, 104)-net over F64, using
(19, 29, 514)-Net in Base 8 — Constructive
(19, 29, 514)-net in base 8, using
- 1 times m-reduction [i] based on (19, 30, 514)-net in base 8, using
- trace code for nets [i] based on (4, 15, 257)-net in base 64, using
- 1 times m-reduction [i] based on (4, 16, 257)-net in base 64, using
- base change [i] based on digital (0, 12, 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, 12, 257)-net over F256, using
- 1 times m-reduction [i] based on (4, 16, 257)-net in base 64, using
- trace code for nets [i] based on (4, 15, 257)-net in base 64, using
(19, 29, 571)-Net over F8 — Digital
Digital (19, 29, 571)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(829, 571, F8, 10) (dual of [571, 542, 11]-code), using
- 52 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 0, 1, 12 times 0, 1, 34 times 0) [i] based on linear OA(825, 515, F8, 10) (dual of [515, 490, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(8) [i] based on
- linear OA(825, 512, F8, 10) (dual of [512, 487, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(822, 512, F8, 9) (dual of [512, 490, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(80, 3, F8, 0) (dual of [3, 3, 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(9) ⊂ Ce(8) [i] based on
- 52 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 0, 1, 12 times 0, 1, 34 times 0) [i] based on linear OA(825, 515, F8, 10) (dual of [515, 490, 11]-code), using
(19, 29, 64363)-Net in Base 8 — Upper bound on s
There is no (19, 29, 64364)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 154 744654 049684 535559 760682 > 829 [i]