Best Known (218−72, 218, s)-Nets in Base 3
(218−72, 218, 162)-Net over F3 — Constructive and digital
Digital (146, 218, 162)-net over F3, using
- 10 times m-reduction [i] based on digital (146, 228, 162)-net over F3, using
- trace code for nets [i] based on digital (32, 114, 81)-net over F9, using
- net from sequence [i] based on digital (32, 80)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- F4 from the tower of function fields by Bezerra and GarcÃa over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- net from sequence [i] based on digital (32, 80)-sequence over F9, using
- trace code for nets [i] based on digital (32, 114, 81)-net over F9, using
(218−72, 218, 353)-Net over F3 — Digital
Digital (146, 218, 353)-net over F3, using
(218−72, 218, 5497)-Net in Base 3 — Upper bound on s
There is no (146, 218, 5498)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 103 341264 357961 341968 262757 847902 533832 322570 427241 066553 401122 604290 410191 139493 580442 025996 628301 735657 > 3218 [i]