Best Known (126, 126+39, s)-Nets in Base 8
(126, 126+39, 1074)-Net over F8 — Constructive and digital
Digital (126, 165, 1074)-net over F8, using
- 81 times duplication [i] based on digital (125, 164, 1074)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (11, 30, 48)-net over F8, using
- net from sequence [i] based on digital (11, 47)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 11 and N(F) ≥ 48, using
- net from sequence [i] based on digital (11, 47)-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 (11, 30, 48)-net over F8, using
- (u, u+v)-construction [i] based on
(126, 126+39, 1090)-Net in Base 8 — Constructive
(126, 165, 1090)-net in base 8, using
- 81 times duplication [i] based on (125, 164, 1090)-net in base 8, using
- (u, u+v)-construction [i] based on
- (33, 52, 514)-net in base 8, using
- base change [i] based on digital (20, 39, 514)-net over F16, using
- 1 times m-reduction [i] based on digital (20, 40, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 20, 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
- trace code for nets [i] based on digital (0, 20, 257)-net over F256, using
- 1 times m-reduction [i] based on digital (20, 40, 514)-net over F16, using
- base change [i] based on digital (20, 39, 514)-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
- (33, 52, 514)-net in base 8, using
- (u, u+v)-construction [i] based on
(126, 126+39, 17926)-Net over F8 — Digital
Digital (126, 165, 17926)-net over F8, using
(126, 126+39, large)-Net in Base 8 — Upper bound on s
There is no (126, 165, large)-net in base 8, because
- 37 times m-reduction [i] would yield (126, 128, large)-net in base 8, but