Best Known (140−41, 140, s)-Nets in Base 9
(140−41, 140, 774)-Net over F9 — Constructive and digital
Digital (99, 140, 774)-net over F9, using
- (u, u+v)-construction [i] based on
- digital (6, 26, 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 (73, 114, 740)-net over F9, using
- trace code for nets [i] based on digital (16, 57, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- trace code for nets [i] based on digital (16, 57, 370)-net over F81, using
- digital (6, 26, 34)-net over F9, using
(140−41, 140, 4331)-Net over F9 — Digital
Digital (99, 140, 4331)-net over F9, using
(140−41, 140, 4448366)-Net in Base 9 — Upper bound on s
There is no (99, 140, 4448367)-net in base 9, because
- 1 times m-reduction [i] would yield (99, 139, 4448367)-net in base 9, but
- the generalized Rao bound for nets shows that 9m ≥ 4 362252 096641 917213 486182 045086 940022 695686 557367 219142 876167 942094 561656 600996 006942 015712 014784 305828 080020 251178 102675 052049 146209 > 9139 [i]