Best Known (71−30, 71, s)-Nets in Base 8
(71−30, 71, 256)-Net over F8 — Constructive and digital
Digital (41, 71, 256)-net over F8, using
- 1 times m-reduction [i] based on digital (41, 72, 256)-net over F8, using
- trace code for nets [i] based on digital (5, 36, 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, 36, 128)-net over F64, using
(71−30, 71, 258)-Net in Base 8 — Constructive
(41, 71, 258)-net in base 8, using
- 81 times duplication [i] based on (40, 70, 258)-net in base 8, using
- trace code for nets [i] based on (5, 35, 129)-net in base 64, using
- base change [i] based on digital (0, 30, 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
- base change [i] based on digital (0, 30, 129)-net over F128, using
- trace code for nets [i] based on (5, 35, 129)-net in base 64, using
(71−30, 71, 278)-Net over F8 — Digital
Digital (41, 71, 278)-net over F8, using
(71−30, 71, 17260)-Net in Base 8 — Upper bound on s
There is no (41, 71, 17261)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 13164 651336 056115 785809 009496 373835 527033 359171 169207 062767 567136 > 871 [i]