Best Known (7, 7+10, s)-Nets in Base 9
(7, 7+10, 36)-Net over F9 — Constructive and digital
Digital (7, 17, 36)-net over F9, using
- net from sequence [i] based on digital (7, 35)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 7 and N(F) ≥ 36, using
(7, 7+10, 38)-Net in Base 9 — Constructive
(7, 17, 38)-net in base 9, using
- 1 times m-reduction [i] based on (7, 18, 38)-net in base 9, using
- base change [i] based on digital (1, 12, 38)-net over F27, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 1 and N(F) ≥ 38, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- base change [i] based on digital (1, 12, 38)-net over F27, using
(7, 7+10, 40)-Net over F9 — Digital
Digital (7, 17, 40)-net over F9, using
- net from sequence [i] based on digital (7, 39)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 7 and N(F) ≥ 40, using
(7, 7+10, 569)-Net in Base 9 — Upper bound on s
There is no (7, 17, 570)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 16811 416112 311953 > 917 [i]