Best Known (129, 129+68, s)-Nets in Base 3
(129, 129+68, 156)-Net over F3 — Constructive and digital
Digital (129, 197, 156)-net over F3, using
- 17 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+68, 282)-Net over F3 — Digital
Digital (129, 197, 282)-net over F3, using
(129, 129+68, 3901)-Net in Base 3 — Upper bound on s
There is no (129, 197, 3902)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 9872 054416 733206 951101 109624 517348 783848 901618 190214 523834 594320 269585 153514 698792 446446 684605 > 3197 [i]