Best Known (99, 99+31, s)-Nets in Base 8
(99, 99+31, 1026)-Net over F8 — Constructive and digital
Digital (99, 130, 1026)-net over F8, using
- 12 times m-reduction [i] based on digital (99, 142, 1026)-net over F8, using
- trace code for nets [i] based on digital (28, 71, 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, 71, 513)-net over F64, using
(99, 99+31, 1032)-Net in Base 8 — Constructive
(99, 130, 1032)-net in base 8, using
- 82 times duplication [i] based on (97, 128, 1032)-net in base 8, using
- base change [i] based on digital (65, 96, 1032)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (17, 32, 516)-net over F16, using
- trace code for nets [i] based on digital (1, 16, 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, 16, 258)-net over F256, using
- digital (33, 64, 516)-net over F16, using
- trace code for nets [i] based on digital (1, 32, 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, 32, 258)-net over F256, using
- digital (17, 32, 516)-net over F16, using
- (u, u+v)-construction [i] based on
- base change [i] based on digital (65, 96, 1032)-net over F16, using
(99, 99+31, 14110)-Net over F8 — Digital
Digital (99, 130, 14110)-net over F8, using
(99, 99+31, large)-Net in Base 8 — Upper bound on s
There is no (99, 130, large)-net in base 8, because
- 29 times m-reduction [i] would yield (99, 101, large)-net in base 8, but