Best Known (70−30, 70, s)-Nets in Base 9
(70−30, 70, 320)-Net over F9 — Constructive and digital
Digital (40, 70, 320)-net over F9, using
- trace code for nets [i] based on digital (5, 35, 160)-net over F81, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 5 and N(F) ≥ 160, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
(70−30, 70, 334)-Net over F9 — Digital
Digital (40, 70, 334)-net over F9, using
- trace code for nets [i] based on digital (5, 35, 167)-net over F81, using
- net from sequence [i] based on digital (5, 166)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 5 and N(F) ≥ 167, using
- net from sequence [i] based on digital (5, 166)-sequence over F81, using
(70−30, 70, 22784)-Net in Base 9 — Upper bound on s
There is no (40, 70, 22785)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 6 267903 856685 652220 496404 156660 324694 264104 784547 067463 628758 683833 > 970 [i]