Best Known (91−51, 91, s)-Nets in Base 9
(91−51, 91, 84)-Net over F9 — Constructive and digital
Digital (40, 91, 84)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (2, 27, 20)-net over F9, using
- net from sequence [i] based on digital (2, 19)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 2 and N(F) ≥ 20, using
- net from sequence [i] based on digital (2, 19)-sequence over F9, using
- digital (13, 64, 64)-net over F9, using
- net from sequence [i] based on digital (13, 63)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 13 and N(F) ≥ 64, using
- net from sequence [i] based on digital (13, 63)-sequence over F9, using
- digital (2, 27, 20)-net over F9, using
(91−51, 91, 88)-Net in Base 9 — Constructive
(40, 91, 88)-net in base 9, using
- 2 times m-reduction [i] based on (40, 93, 88)-net in base 9, using
- base change [i] based on digital (9, 62, 88)-net over F27, using
- net from sequence [i] based on digital (9, 87)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 9 and N(F) ≥ 88, using
- net from sequence [i] based on digital (9, 87)-sequence over F27, using
- base change [i] based on digital (9, 62, 88)-net over F27, using
(91−51, 91, 140)-Net over F9 — Digital
Digital (40, 91, 140)-net over F9, using
- t-expansion [i] based on digital (39, 91, 140)-net over F9, using
- net from sequence [i] based on digital (39, 139)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 39 and N(F) ≥ 140, using
- net from sequence [i] based on digital (39, 139)-sequence over F9, using
(91−51, 91, 3450)-Net in Base 9 — Upper bound on s
There is no (40, 91, 3451)-net in base 9, because
- 1 times m-reduction [i] would yield (40, 90, 3451)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 76 321693 240606 906382 124692 826073 964890 327393 172399 210883 756613 797132 513355 501834 577433 > 990 [i]