Best Known (143, 143+98, s)-Nets in Base 3
(143, 143+98, 156)-Net over F3 — Constructive and digital
Digital (143, 241, 156)-net over F3, using
- 1 times m-reduction [i] based on digital (143, 242, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 121, 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, 121, 78)-net over F9, using
(143, 143+98, 210)-Net over F3 — Digital
Digital (143, 241, 210)-net over F3, using
(143, 143+98, 2074)-Net in Base 3 — Upper bound on s
There is no (143, 241, 2075)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 9 712928 310091 704948 543763 454030 823745 675368 697347 865182 441732 996354 582472 480234 815222 171886 434867 296543 385465 056087 > 3241 [i]