Best Known (57−32, 57, s)-Nets in Base 128
(57−32, 57, 417)-Net over F128 — Constructive and digital
Digital (25, 57, 417)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (0, 16, 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, 41, 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, 16, 129)-net over F128, using
(57−32, 57, 515)-Net in Base 128 — Constructive
(25, 57, 515)-net in base 128, using
- 1 times m-reduction [i] based on (25, 58, 515)-net in base 128, using
- (u, u+v)-construction [i] based on
- (3, 19, 257)-net in base 128, using
- 5 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
- 5 times m-reduction [i] based on (3, 24, 257)-net in base 128, using
- (6, 39, 258)-net in base 128, using
- 1 times m-reduction [i] based on (6, 40, 258)-net in base 128, using
- base change [i] based on digital (1, 35, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- base change [i] based on digital (1, 35, 258)-net over F256, using
- 1 times m-reduction [i] based on (6, 40, 258)-net in base 128, using
- (3, 19, 257)-net in base 128, using
- (u, u+v)-construction [i] based on
(57−32, 57, 748)-Net over F128 — Digital
Digital (25, 57, 748)-net over F128, using
(57−32, 57, 1720555)-Net in Base 128 — Upper bound on s
There is no (25, 57, 1720556)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 1 291135 252546 855167 414201 345398 163270 024314 268902 829861 756046 954094 611888 680992 849261 960219 266890 919054 708239 095515 847358 > 12857 [i]