Best Known (144, 144+92, s)-Nets in Base 3
(144, 144+92, 156)-Net over F3 — Constructive and digital
Digital (144, 236, 156)-net over F3, using
- 8 times m-reduction [i] based on digital (144, 244, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 122, 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, 122, 78)-net over F9, using
(144, 144+92, 232)-Net over F3 — Digital
Digital (144, 236, 232)-net over F3, using
(144, 144+92, 2478)-Net in Base 3 — Upper bound on s
There is no (144, 236, 2479)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 40197 132502 576368 798436 887508 264073 441314 422327 672824 889957 010490 209749 977652 066187 570063 309515 999232 580661 299589 > 3236 [i]