Best Known (70−34, 70, s)-Nets in Base 8
(70−34, 70, 160)-Net over F8 — Constructive and digital
Digital (36, 70, 160)-net over F8, using
- trace code for nets [i] based on digital (1, 35, 80)-net over F64, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
(70−34, 70, 162)-Net over F8 — Digital
Digital (36, 70, 162)-net over F8, using
- trace code for nets [i] based on digital (1, 35, 81)-net over F64, using
- net from sequence [i] based on digital (1, 80)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 81, using
- net from sequence [i] based on digital (1, 80)-sequence over F64, using
(70−34, 70, 5353)-Net in Base 8 — Upper bound on s
There is no (36, 70, 5354)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 1650 016679 830570 960258 569155 132681 104245 761692 436335 265349 515074 > 870 [i]