Best Known (30, 30+37, s)-Nets in Base 128
(30, 30+37, 480)-Net over F128 — Constructive and digital
Digital (30, 67, 480)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (3, 21, 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, 46, 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, 21, 192)-net over F128, using
(30, 30+37, 545)-Net in Base 128 — Constructive
(30, 67, 545)-net in base 128, using
- (u, u+v)-construction [i] based on
- (3, 21, 257)-net in base 128, using
- 3 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
- 3 times m-reduction [i] based on (3, 24, 257)-net in base 128, using
- digital (9, 46, 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, 21, 257)-net in base 128, using
(30, 30+37, 957)-Net over F128 — Digital
Digital (30, 67, 957)-net over F128, using
(30, 30+37, 3167828)-Net in Base 128 — Upper bound on s
There is no (30, 67, 3167829)-net in base 128, because
- 1 times m-reduction [i] would yield (30, 66, 3167829)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 11 908537 450685 452165 745651 566653 114871 581451 159681 232685 157889 517155 374140 620231 717600 783887 724492 033934 787338 159767 623439 128446 187976 740870 > 12866 [i]