Best Known (216−80, 216, s)-Nets in Base 3
(216−80, 216, 156)-Net over F3 — Constructive and digital
Digital (136, 216, 156)-net over F3, using
- 12 times m-reduction [i] based on digital (136, 228, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 114, 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, 114, 78)-net over F9, using
(216−80, 216, 249)-Net over F3 — Digital
Digital (136, 216, 249)-net over F3, using
(216−80, 216, 2933)-Net in Base 3 — Upper bound on s
There is no (136, 216, 2934)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 11 455174 666788 718625 765439 265971 159230 044865 985092 451128 172947 697889 625131 105410 603649 142822 932654 366737 > 3216 [i]