Best Known (58−31, 58, s)-Nets in Base 128
(58−31, 58, 480)-Net over F128 — Constructive and digital
Digital (27, 58, 480)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (3, 18, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- digital (9, 40, 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 (3, 18, 192)-net over F128, using
(58−31, 58, 545)-Net in Base 128 — Constructive
(27, 58, 545)-net in base 128, using
- (u, u+v)-construction [i] based on
- (3, 18, 257)-net in base 128, using
- 6 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
- 6 times m-reduction [i] based on (3, 24, 257)-net in base 128, using
- digital (9, 40, 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
- (3, 18, 257)-net in base 128, using
(58−31, 58, 1139)-Net over F128 — Digital
Digital (27, 58, 1139)-net over F128, using
(58−31, 58, 5144701)-Net in Base 128 — Upper bound on s
There is no (27, 58, 5144702)-net in base 128, because
- 1 times m-reduction [i] would yield (27, 57, 5144702)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 1 291125 845720 266104 838487 253088 092419 379125 523245 139489 706228 215618 178476 669871 967904 533962 810623 665847 165015 056936 396232 > 12857 [i]