Best Known (67−42, 67, s)-Nets in Base 9
(67−42, 67, 78)-Net over F9 — Constructive and digital
Digital (25, 67, 78)-net over F9, using
- t-expansion [i] based on digital (22, 67, 78)-net over F9, using
- net from sequence [i] based on digital (22, 77)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- F3 from the tower of function fields by GarcÃa and Stichtenoth over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 22 and N(F) ≥ 78, using
- net from sequence [i] based on digital (22, 77)-sequence over F9, using
(67−42, 67, 96)-Net over F9 — Digital
Digital (25, 67, 96)-net over F9, using
- net from sequence [i] based on digital (25, 95)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 25 and N(F) ≥ 96, using
(67−42, 67, 1189)-Net in Base 9 — Upper bound on s
There is no (25, 67, 1190)-net in base 9, because
- the generalized Rao bound for nets shows that 9m ≥ 8689 203521 737043 202710 178645 252145 024642 178522 421034 991041 209201 > 967 [i]