Best Known (67−39, 67, s)-Nets in Base 128
(67−39, 67, 417)-Net over F128 — Constructive and digital
Digital (28, 67, 417)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (0, 19, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 0 and N(F) ≥ 129, using
- the rational function field F128(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- 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
- digital (0, 19, 129)-net over F128, using
(67−39, 67, 514)-Net in Base 128 — Constructive
(28, 67, 514)-net in base 128, using
- (u, u+v)-construction [i] based on
- (3, 22, 257)-net in base 128, using
- 2 times m-reduction [i] based on (3, 24, 257)-net in base 128, 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
- 2 times m-reduction [i] based on (3, 24, 257)-net in base 128, using
- (6, 45, 257)-net in base 128, using
- 3 times m-reduction [i] based on (6, 48, 257)-net in base 128, 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 (see above)
- base change [i] based on digital (0, 42, 257)-net over F256, using
- 3 times m-reduction [i] based on (6, 48, 257)-net in base 128, using
- (3, 22, 257)-net in base 128, using
(67−39, 67, 633)-Net over F128 — Digital
Digital (28, 67, 633)-net over F128, using
(67−39, 67, 1303739)-Net in Base 128 — Upper bound on s
There is no (28, 67, 1303740)-net in base 128, because
- 1 times m-reduction [i] would yield (28, 66, 1303740)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 11 908657 417845 968504 315526 879730 126460 539693 257655 669145 005156 460069 933459 311432 499969 012105 535106 377688 241477 120367 366237 239724 266354 818331 > 12866 [i]