Best Known (57, 130, s)-Nets in Base 8
(57, 130, 99)-Net over F8 — Constructive and digital
Digital (57, 130, 99)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (7, 43, 34)-net over F8, using
- net from sequence [i] based on digital (7, 33)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 7 and N(F) ≥ 34, using
- net from sequence [i] based on digital (7, 33)-sequence over F8, using
- digital (14, 87, 65)-net over F8, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- the Suzuki function field over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
- digital (7, 43, 34)-net over F8, using
(57, 130, 144)-Net over F8 — Digital
Digital (57, 130, 144)-net over F8, using
- t-expansion [i] based on digital (45, 130, 144)-net over F8, using
- net from sequence [i] based on digital (45, 143)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 45 and N(F) ≥ 144, using
- net from sequence [i] based on digital (45, 143)-sequence over F8, using
(57, 130, 3490)-Net in Base 8 — Upper bound on s
There is no (57, 130, 3491)-net in base 8, because
- 1 times m-reduction [i] would yield (57, 129, 3491)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 316 279030 502217 306763 460527 207070 037481 834549 975895 676623 838175 341018 283232 612287 154032 656325 264315 551362 490740 444896 > 8129 [i]