Best Known (70−55, 70, s)-Nets in Base 128
(70−55, 70, 288)-Net over F128 — Constructive and digital
Digital (15, 70, 288)-net over F128, using
- t-expansion [i] based on digital (9, 70, 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
(70−55, 70, 386)-Net over F128 — Digital
Digital (15, 70, 386)-net over F128, using
- net from sequence [i] based on digital (15, 385)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 15 and N(F) ≥ 386, using
(70−55, 70, 20865)-Net in Base 128 — Upper bound on s
There is no (15, 70, 20866)-net in base 128, because
- 1 times m-reduction [i] would yield (15, 69, 20866)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 25 003334 303255 083460 044913 545634 390416 828636 870749 802236 759442 030839 238318 238612 172869 471326 844745 963227 095596 912367 771493 194435 551452 420868 757824 > 12869 [i]