Best Known (34, 57, s)-Nets in Base 8
(34, 57, 256)-Net over F8 — Constructive and digital
Digital (34, 57, 256)-net over F8, using
- 1 times m-reduction [i] based on digital (34, 58, 256)-net over F8, using
- trace code for nets [i] based on digital (5, 29, 128)-net over F64, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 5 and N(F) ≥ 128, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- trace code for nets [i] based on digital (5, 29, 128)-net over F64, using
(34, 57, 295)-Net over F8 — Digital
Digital (34, 57, 295)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(857, 295, F8, 23) (dual of [295, 238, 24]-code), using
- 34 step Varšamov–Edel lengthening with (ri) = (1, 0, 1, 10 times 0, 1, 20 times 0) [i] based on linear OA(854, 258, F8, 23) (dual of [258, 204, 24]-code), using
- trace code [i] based on linear OA(6427, 129, F64, 23) (dual of [129, 102, 24]-code), using
- extended algebraic-geometric code AGe(F,105P) [i] based on function field F/F64 with g(F) = 4 and N(F) ≥ 129, using
- trace code [i] based on linear OA(6427, 129, F64, 23) (dual of [129, 102, 24]-code), using
- 34 step Varšamov–Edel lengthening with (ri) = (1, 0, 1, 10 times 0, 1, 20 times 0) [i] based on linear OA(854, 258, F8, 23) (dual of [258, 204, 24]-code), using
(34, 57, 300)-Net in Base 8 — Constructive
(34, 57, 300)-net in base 8, using
- 81 times duplication [i] based on (33, 56, 300)-net in base 8, using
- trace code for nets [i] based on (5, 28, 150)-net in base 64, using
- base change [i] based on digital (1, 24, 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
- base change [i] based on digital (1, 24, 150)-net over F128, using
- trace code for nets [i] based on (5, 28, 150)-net in base 64, using
(34, 57, 27756)-Net in Base 8 — Upper bound on s
There is no (34, 57, 27757)-net in base 8, because
- 1 times m-reduction [i] would yield (34, 56, 27757)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 374 240931 463237 445646 736465 623785 388947 347046 985140 > 856 [i]