Best Known (243−120, 243, s)-Nets in Base 3
(243−120, 243, 78)-Net over F3 — Constructive and digital
Digital (123, 243, 78)-net over F3, using
- t-expansion [i] based on digital (121, 243, 78)-net over F3, using
- net from sequence [i] based on digital (121, 77)-sequence over F3, using
- base reduction for sequences [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
- base reduction for sequences [i] based on digital (22, 77)-sequence over F9, using
- net from sequence [i] based on digital (121, 77)-sequence over F3, using
(243−120, 243, 123)-Net over F3 — Digital
Digital (123, 243, 123)-net over F3, using
(243−120, 243, 934)-Net in Base 3 — Upper bound on s
There is no (123, 243, 935)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 91 240953 824427 145533 684606 991965 332041 709449 584909 311496 013136 687227 401816 060820 373795 438670 583407 664229 031937 665417 > 3243 [i]