Best Known (117−28, 117, s)-Nets in Base 8
(117−28, 117, 1026)-Net over F8 — Constructive and digital
Digital (89, 117, 1026)-net over F8, using
- 5 times m-reduction [i] based on digital (89, 122, 1026)-net over F8, using
- trace code for nets [i] based on digital (28, 61, 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, 61, 513)-net over F64, using
(117−28, 117, 1030)-Net in Base 8 — Constructive
(89, 117, 1030)-net in base 8, using
- 1 times m-reduction [i] based on (89, 118, 1030)-net in base 8, using
- (u, u+v)-construction [i] based on
- (24, 38, 514)-net in base 8, using
- trace code for nets [i] based on (5, 19, 257)-net in base 64, using
- 1 times m-reduction [i] based on (5, 20, 257)-net in base 64, using
- base change [i] based on digital (0, 15, 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
- base change [i] based on digital (0, 15, 257)-net over F256, using
- 1 times m-reduction [i] based on (5, 20, 257)-net in base 64, using
- trace code for nets [i] based on (5, 19, 257)-net in base 64, using
- (51, 80, 516)-net in base 8, using
- base change [i] based on digital (31, 60, 516)-net over F16, using
- trace code for nets [i] based on digital (1, 30, 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, 30, 258)-net over F256, using
- base change [i] based on digital (31, 60, 516)-net over F16, using
- (24, 38, 514)-net in base 8, using
- (u, u+v)-construction [i] based on
(117−28, 117, 12798)-Net over F8 — Digital
Digital (89, 117, 12798)-net over F8, using
(117−28, 117, large)-Net in Base 8 — Upper bound on s
There is no (89, 117, large)-net in base 8, because
- 26 times m-reduction [i] would yield (89, 91, large)-net in base 8, but