Best Known (74, 74+30, s)-Nets in Base 8
(74, 74+30, 484)-Net over F8 — Constructive and digital
Digital (74, 104, 484)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (15, 30, 130)-net over F8, using
- trace code for nets [i] based on digital (0, 15, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 0 and N(F) ≥ 65, using
- the rational function field F64(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- trace code for nets [i] based on digital (0, 15, 65)-net over F64, using
- digital (44, 74, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 37, 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, 37, 177)-net over F64, using
- digital (15, 30, 130)-net over F8, using
(74, 74+30, 576)-Net in Base 8 — Constructive
(74, 104, 576)-net in base 8, using
- t-expansion [i] based on (73, 104, 576)-net in base 8, using
- 8 times m-reduction [i] based on (73, 112, 576)-net in base 8, using
- trace code for nets [i] based on (17, 56, 288)-net in base 64, using
- base change [i] based on digital (9, 48, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- base change [i] based on digital (9, 48, 288)-net over F128, using
- trace code for nets [i] based on (17, 56, 288)-net in base 64, using
- 8 times m-reduction [i] based on (73, 112, 576)-net in base 8, using
(74, 74+30, 2903)-Net over F8 — Digital
Digital (74, 104, 2903)-net over F8, using
(74, 74+30, 1675290)-Net in Base 8 — Upper bound on s
There is no (74, 104, 1675291)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 8343 732495 777401 871238 198917 561505 146299 505859 566361 609443 381169 034441 551147 426333 465918 802960 > 8104 [i]