Best Known (170−39, 170, s)-Nets in Base 8
(170−39, 170, 1091)-Net over F8 — Constructive and digital
Digital (131, 170, 1091)-net over F8, using
- 2 times m-reduction [i] based on digital (131, 172, 1091)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (14, 34, 65)-net over F8, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- the Suzuki function field over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
- digital (97, 138, 1026)-net over F8, using
- trace code for nets [i] based on digital (28, 69, 513)-net over F64, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- the Hermitian function field over F64 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- trace code for nets [i] based on digital (28, 69, 513)-net over F64, using
- digital (14, 34, 65)-net over F8, using
- (u, u+v)-construction [i] based on
(170−39, 170, 1094)-Net in Base 8 — Constructive
(131, 170, 1094)-net in base 8, using
- 82 times duplication [i] based on (129, 168, 1094)-net in base 8, using
- (u, u+v)-construction [i] based on
- (37, 56, 518)-net in base 8, using
- base change [i] based on digital (23, 42, 518)-net over F16, using
- trace code for nets [i] based on digital (2, 21, 259)-net over F256, using
- net from sequence [i] based on digital (2, 258)-sequence over F256, using
- trace code for nets [i] based on digital (2, 21, 259)-net over F256, using
- base change [i] based on digital (23, 42, 518)-net over F16, using
- (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
- (37, 56, 518)-net in base 8, using
- (u, u+v)-construction [i] based on
(170−39, 170, 23561)-Net over F8 — Digital
Digital (131, 170, 23561)-net over F8, using
(170−39, 170, large)-Net in Base 8 — Upper bound on s
There is no (131, 170, large)-net in base 8, because
- 37 times m-reduction [i] would yield (131, 133, large)-net in base 8, but