Best Known (128, 128+68, s)-Nets in Base 3
(128, 128+68, 156)-Net over F3 — Constructive and digital
Digital (128, 196, 156)-net over F3, using
- 16 times m-reduction [i] based on digital (128, 212, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 106, 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, 106, 78)-net over F9, using
(128, 128+68, 277)-Net over F3 — Digital
Digital (128, 196, 277)-net over F3, using
(128, 128+68, 3776)-Net in Base 3 — Upper bound on s
There is no (128, 196, 3777)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 3294 333947 040008 489078 966755 908851 751279 875682 349254 342308 096899 595670 164892 613066 245543 630345 > 3196 [i]