Best Known (129, 129+76, s)-Nets in Base 3
(129, 129+76, 156)-Net over F3 — Constructive and digital
Digital (129, 205, 156)-net over F3, using
- 9 times m-reduction [i] based on digital (129, 214, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 107, 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
- trace code for nets [i] based on digital (22, 107, 78)-net over F9, using
(129, 129+76, 237)-Net over F3 — Digital
Digital (129, 205, 237)-net over F3, using
(129, 129+76, 2779)-Net in Base 3 — Upper bound on s
There is no (129, 205, 2780)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 65 198330 688696 674402 613643 430798 737968 057297 741633 562700 231291 740586 086038 019065 918094 389147 769065 > 3205 [i]