Best Known (44, 44+20, s)-Nets in Base 8
(44, 44+20, 363)-Net over F8 — Constructive and digital
Digital (44, 64, 363)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (0, 10, 9)-net over F8, using
- net from sequence [i] based on digital (0, 8)-sequence over F8, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 0 and N(F) ≥ 9, using
- the rational function field F8(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 8)-sequence over F8, using
- digital (34, 54, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 27, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- trace code for nets [i] based on digital (7, 27, 177)-net over F64, using
- digital (0, 10, 9)-net over F8, using
(44, 44+20, 523)-Net in Base 8 — Constructive
(44, 64, 523)-net in base 8, using
- (u, u+v)-construction [i] based on
- digital (0, 10, 9)-net over F8, using
- net from sequence [i] based on digital (0, 8)-sequence over F8, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 0 and N(F) ≥ 9, using
- the rational function field F8(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 8)-sequence over F8, using
- (34, 54, 514)-net in base 8, using
- trace code for nets [i] based on (7, 27, 257)-net in base 64, using
- 1 times m-reduction [i] based on (7, 28, 257)-net in base 64, using
- base change [i] based on digital (0, 21, 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, 21, 257)-net over F256, using
- 1 times m-reduction [i] based on (7, 28, 257)-net in base 64, using
- trace code for nets [i] based on (7, 27, 257)-net in base 64, using
- digital (0, 10, 9)-net over F8, using
(44, 44+20, 1257)-Net over F8 — Digital
Digital (44, 64, 1257)-net over F8, using
(44, 44+20, 389625)-Net in Base 8 — Upper bound on s
There is no (44, 64, 389626)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 6277 153490 257261 956728 278731 549135 336098 885186 892187 948824 > 864 [i]