Best Known (177−62, 177, s)-Nets in Base 3
(177−62, 177, 156)-Net over F3 — Constructive and digital
Digital (115, 177, 156)-net over F3, using
- 9 times m-reduction [i] based on digital (115, 186, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 93, 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, 93, 78)-net over F9, using
(177−62, 177, 247)-Net over F3 — Digital
Digital (115, 177, 247)-net over F3, using
(177−62, 177, 3259)-Net in Base 3 — Upper bound on s
There is no (115, 177, 3260)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 2 828433 426791 424671 211719 319972 445308 120445 154736 071782 898611 752701 704570 476438 196305 > 3177 [i]