Best Known (129, 129+78, s)-Nets in Base 3
(129, 129+78, 156)-Net over F3 — Constructive and digital
Digital (129, 207, 156)-net over F3, using
- 7 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+78, 229)-Net over F3 — Digital
Digital (129, 207, 229)-net over F3, using
(129, 129+78, 2584)-Net in Base 3 — Upper bound on s
There is no (129, 207, 2585)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 582 687128 672641 912505 118359 505741 509997 842572 900831 644844 965807 696413 735116 856443 491068 510964 627819 > 3207 [i]