Best Known (128, 128+39, s)-Nets in Base 8
(128, 128+39, 1091)-Net over F8 — Constructive and digital
Digital (128, 167, 1091)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (14, 33, 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 (95, 134, 1026)-net over F8, using
- trace code for nets [i] based on digital (28, 67, 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, 67, 513)-net over F64, using
- digital (14, 33, 65)-net over F8, using
(128, 128+39, 1092)-Net in Base 8 — Constructive
(128, 167, 1092)-net in base 8, using
- 81 times duplication [i] based on (127, 166, 1092)-net in base 8, using
- (u, u+v)-construction [i] based on
- (35, 54, 516)-net in base 8, using
- trace code for nets [i] based on (8, 27, 258)-net in base 64, using
- 1 times m-reduction [i] based on (8, 28, 258)-net in base 64, using
- base change [i] based on digital (1, 21, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- base change [i] based on digital (1, 21, 258)-net over F256, using
- 1 times m-reduction [i] based on (8, 28, 258)-net in base 64, using
- trace code for nets [i] based on (8, 27, 258)-net in base 64, 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
- (35, 54, 516)-net in base 8, using
- (u, u+v)-construction [i] based on
(128, 128+39, 19997)-Net over F8 — Digital
Digital (128, 167, 19997)-net over F8, using
(128, 128+39, large)-Net in Base 8 — Upper bound on s
There is no (128, 167, large)-net in base 8, because
- 37 times m-reduction [i] would yield (128, 130, large)-net in base 8, but