Best Known (55, 55+65, s)-Nets in Base 9
(55, 55+65, 108)-Net over F9 — Constructive and digital
Digital (55, 120, 108)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (6, 38, 34)-net over F9, using
- net from sequence [i] based on digital (6, 33)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 6 and N(F) ≥ 34, using
- net from sequence [i] based on digital (6, 33)-sequence over F9, using
- digital (17, 82, 74)-net over F9, using
- net from sequence [i] based on digital (17, 73)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 17 and N(F) ≥ 74, using
- net from sequence [i] based on digital (17, 73)-sequence over F9, using
- digital (6, 38, 34)-net over F9, using
(55, 55+65, 182)-Net over F9 — Digital
Digital (55, 120, 182)-net over F9, using
- t-expansion [i] based on digital (50, 120, 182)-net over F9, using
- net from sequence [i] based on digital (50, 181)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 50 and N(F) ≥ 182, using
- net from sequence [i] based on digital (50, 181)-sequence over F9, using
(55, 55+65, 5634)-Net in Base 9 — Upper bound on s
There is no (55, 120, 5635)-net in base 9, because
- 1 times m-reduction [i] would yield (55, 119, 5635)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 359148 227747 593900 852778 102257 553431 829896 386170 841407 028058 015779 283917 484101 605624 939956 360171 378595 777693 149953 > 9119 [i]