Best Known (7, 7+29, s)-Nets in Base 9
(7, 7+29, 36)-Net over F9 — Constructive and digital
Digital (7, 36, 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+29, 40)-Net over F9 — Digital
Digital (7, 36, 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+29, 175)-Net in Base 9 — Upper bound on s
There is no (7, 36, 176)-net in base 9, because
- 1 times m-reduction [i] would yield (7, 35, 176)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 2599 357120 081446 669232 963160 948481 > 935 [i]