Best Known (129, 214, s)-Nets in Base 3
(129, 214, 156)-Net over F3 — Constructive and digital
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
(129, 214, 202)-Net over F3 — Digital
Digital (129, 214, 202)-net over F3, using
(129, 214, 2128)-Net in Base 3 — Upper bound on s
There is no (129, 214, 2129)-net in base 3, because
- 1 times m-reduction [i] would yield (129, 213, 2129)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 424949 851964 057090 549629 033559 960251 372479 400255 324117 425899 835626 066554 353772 998800 144141 976894 435657 > 3213 [i]