Best Known (137−33, 137, s)-Nets in Base 8
(137−33, 137, 1026)-Net over F8 — Constructive and digital
Digital (104, 137, 1026)-net over F8, using
- 15 times m-reduction [i] based on digital (104, 152, 1026)-net over F8, using
- trace code for nets [i] based on digital (28, 76, 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, 76, 513)-net over F64, using
(137−33, 137, 1032)-Net in Base 8 — Constructive
(104, 137, 1032)-net in base 8, using
- 81 times duplication [i] based on (103, 136, 1032)-net in base 8, using
- base change [i] based on digital (69, 102, 1032)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (18, 34, 516)-net over F16, using
- trace code for nets [i] based on digital (1, 17, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- trace code for nets [i] based on digital (1, 17, 258)-net over F256, using
- digital (35, 68, 516)-net over F16, using
- trace code for nets [i] based on digital (1, 34, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256 (see above)
- trace code for nets [i] based on digital (1, 34, 258)-net over F256, using
- digital (18, 34, 516)-net over F16, using
- (u, u+v)-construction [i] based on
- base change [i] based on digital (69, 102, 1032)-net over F16, using
(137−33, 137, 13448)-Net over F8 — Digital
Digital (104, 137, 13448)-net over F8, using
(137−33, 137, large)-Net in Base 8 — Upper bound on s
There is no (104, 137, large)-net in base 8, because
- 31 times m-reduction [i] would yield (104, 106, large)-net in base 8, but