Best Known (127−71, 127, s)-Nets in Base 8
(127−71, 127, 99)-Net over F8 — Constructive and digital
Digital (56, 127, 99)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (7, 42, 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, 85, 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, 42, 34)-net over F8, using
(127−71, 127, 144)-Net over F8 — Digital
Digital (56, 127, 144)-net over F8, using
- t-expansion [i] based on digital (45, 127, 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
(127−71, 127, 3520)-Net in Base 8 — Upper bound on s
There is no (56, 127, 3521)-net in base 8, because
- 1 times m-reduction [i] would yield (56, 126, 3521)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 619455 567647 679455 319302 201851 204440 955470 616163 130159 463926 495120 107149 598685 036633 529715 929744 680170 985041 498688 > 8126 [i]