Best Known (109−40, 109, s)-Nets in Base 8
(109−40, 109, 354)-Net over F8 — Constructive and digital
Digital (69, 109, 354)-net over F8, using
- 15 times m-reduction [i] based on digital (69, 124, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 62, 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, 62, 177)-net over F64, using
(109−40, 109, 514)-Net in Base 8 — Constructive
(69, 109, 514)-net in base 8, using
- 1 times m-reduction [i] based on (69, 110, 514)-net in base 8, using
- trace code for nets [i] based on (14, 55, 257)-net in base 64, using
- 1 times m-reduction [i] based on (14, 56, 257)-net in base 64, using
- base change [i] based on digital (0, 42, 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, 42, 257)-net over F256, using
- 1 times m-reduction [i] based on (14, 56, 257)-net in base 64, using
- trace code for nets [i] based on (14, 55, 257)-net in base 64, using
(109−40, 109, 755)-Net over F8 — Digital
Digital (69, 109, 755)-net over F8, using
(109−40, 109, 99081)-Net in Base 8 — Upper bound on s
There is no (69, 109, 99082)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 273 410150 087005 469054 253101 018067 006323 107057 725257 398258 395086 595490 243726 633119 474091 192073 076832 > 8109 [i]