Best Known (70−39, 70, s)-Nets in Base 128
(70−39, 70, 480)-Net over F128 — Constructive and digital
Digital (31, 70, 480)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (3, 22, 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, 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 (3, 22, 192)-net over F128, using
(70−39, 70, 545)-Net in Base 128 — Constructive
(31, 70, 545)-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
- 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
- (3, 22, 257)-net in base 128, using
(70−39, 70, 920)-Net over F128 — Digital
Digital (31, 70, 920)-net over F128, using
(70−39, 70, 2804850)-Net in Base 128 — Upper bound on s
There is no (31, 70, 2804851)-net in base 128, because
- 1 times m-reduction [i] would yield (31, 69, 2804851)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 24 974057 581205 738074 436032 052788 975871 627412 324459 375860 986379 003548 485624 550998 590163 287946 353930 022246 999212 808207 234859 508053 482457 155576 377632 > 12869 [i]