Best Known (129, 129+74, s)-Nets in Base 3
(129, 129+74, 156)-Net over F3 — Constructive and digital
Digital (129, 203, 156)-net over F3, using
- 11 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+74, 247)-Net over F3 — Digital
Digital (129, 203, 247)-net over F3, using
(129, 129+74, 3001)-Net in Base 3 — Upper bound on s
There is no (129, 203, 3002)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 7 191223 890402 205607 647144 586518 126337 210974 341396 365677 707149 919208 407552 952723 091390 435223 294477 > 3203 [i]