Best Known (43, 43+30, s)-Nets in Base 8
(43, 43+30, 256)-Net over F8 — Constructive and digital
Digital (43, 73, 256)-net over F8, using
- 3 times m-reduction [i] based on digital (43, 76, 256)-net over F8, using
- trace code for nets [i] based on digital (5, 38, 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, 38, 128)-net over F64, using
(43, 43+30, 258)-Net in Base 8 — Constructive
(43, 73, 258)-net in base 8, using
- 1 times m-reduction [i] based on (43, 74, 258)-net in base 8, using
- trace code for nets [i] based on (6, 37, 129)-net in base 64, using
- 5 times m-reduction [i] based on (6, 42, 129)-net in base 64, using
- base change [i] based on digital (0, 36, 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, 36, 129)-net over F128, using
- 5 times m-reduction [i] based on (6, 42, 129)-net in base 64, using
- trace code for nets [i] based on (6, 37, 129)-net in base 64, using
(43, 43+30, 325)-Net over F8 — Digital
Digital (43, 73, 325)-net over F8, using
(43, 43+30, 22778)-Net in Base 8 — Upper bound on s
There is no (43, 73, 22779)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 842567 410831 555464 372081 593372 761723 189076 578150 728045 071076 445872 > 873 [i]