Best Known (7, 7+13, s)-Nets in Base 9
(7, 7+13, 36)-Net over F9 — Constructive and digital
Digital (7, 20, 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+13, 40)-Net over F9 — Digital
Digital (7, 20, 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+13, 390)-Net in Base 9 — Upper bound on s
There is no (7, 20, 391)-net in base 9, because
- 1 times m-reduction [i] would yield (7, 19, 391)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 1 367029 772325 413457 > 919 [i]