Best Known (110−59, 110, s)-Nets in Base 9
(110−59, 110, 106)-Net over F9 — Constructive and digital
Digital (51, 110, 106)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (5, 34, 32)-net over F9, using
- net from sequence [i] based on digital (5, 31)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 5 and N(F) ≥ 32, using
- net from sequence [i] based on digital (5, 31)-sequence over F9, using
- digital (17, 76, 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 (5, 34, 32)-net over F9, using
(110−59, 110, 182)-Net over F9 — Digital
Digital (51, 110, 182)-net over F9, using
- t-expansion [i] based on digital (50, 110, 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
(110−59, 110, 5614)-Net in Base 9 — Upper bound on s
There is no (51, 110, 5615)-net in base 9, because
- 1 times m-reduction [i] would yield (51, 109, 5615)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 103 192611 478667 260492 396901 470445 295663 391461 122313 512844 026814 433881 265419 360250 007614 986606 674541 063321 > 9109 [i]