Best Known (201−70, 201, s)-Nets in Base 3
(201−70, 201, 156)-Net over F3 — Constructive and digital
Digital (131, 201, 156)-net over F3, using
- 17 times m-reduction [i] based on digital (131, 218, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 109, 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, 109, 78)-net over F9, using
(201−70, 201, 280)-Net over F3 — Digital
Digital (131, 201, 280)-net over F3, using
(201−70, 201, 3787)-Net in Base 3 — Upper bound on s
There is no (131, 201, 3788)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 800690 779887 189642 533978 774937 931450 445599 294931 179170 448972 464197 835413 668300 162271 481996 159825 > 3201 [i]