Best Known (84, 84+29, s)-Nets in Base 8
(84, 84+29, 610)-Net over F8 — Constructive and digital
Digital (84, 113, 610)-net over F8, using
- 1 times m-reduction [i] based on digital (84, 114, 610)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (25, 40, 256)-net over F8, using
- trace code for nets [i] based on digital (5, 20, 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, 20, 128)-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 (25, 40, 256)-net over F8, using
- (u, u+v)-construction [i] based on
(84, 84+29, 772)-Net in Base 8 — Constructive
(84, 113, 772)-net in base 8, using
- 81 times duplication [i] based on (83, 112, 772)-net in base 8, using
- (u, u+v)-construction [i] based on
- (20, 34, 258)-net in base 8, using
- trace code for nets [i] based on (3, 17, 129)-net in base 64, using
- 4 times m-reduction [i] based on (3, 21, 129)-net in base 64, using
- base change [i] based on digital (0, 18, 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, 18, 129)-net over F128, using
- 4 times m-reduction [i] based on (3, 21, 129)-net in base 64, using
- trace code for nets [i] based on (3, 17, 129)-net in base 64, using
- (49, 78, 514)-net in base 8, using
- trace code for nets [i] based on (10, 39, 257)-net in base 64, using
- 1 times m-reduction [i] based on (10, 40, 257)-net in base 64, using
- base change [i] based on digital (0, 30, 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, 30, 257)-net over F256, using
- 1 times m-reduction [i] based on (10, 40, 257)-net in base 64, using
- trace code for nets [i] based on (10, 39, 257)-net in base 64, using
- (20, 34, 258)-net in base 8, using
- (u, u+v)-construction [i] based on
(84, 84+29, 7135)-Net over F8 — Digital
Digital (84, 113, 7135)-net over F8, using
(84, 84+29, large)-Net in Base 8 — Upper bound on s
There is no (84, 113, large)-net in base 8, because
- 27 times m-reduction [i] would yield (84, 86, large)-net in base 8, but