Best Known (141, 141+92, s)-Nets in Base 3
(141, 141+92, 156)-Net over F3 — Constructive and digital
Digital (141, 233, 156)-net over F3, using
- 5 times m-reduction [i] based on digital (141, 238, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 119, 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, 119, 78)-net over F9, using
(141, 141+92, 221)-Net over F3 — Digital
Digital (141, 233, 221)-net over F3, using
(141, 141+92, 2304)-Net in Base 3 — Upper bound on s
There is no (141, 233, 2305)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 1503 453461 223747 318662 075490 341757 514240 055312 016411 131860 720224 647313 517571 940692 117785 909169 307916 328157 097977 > 3233 [i]