Best Known (158−51, 158, s)-Nets in Base 3
(158−51, 158, 156)-Net over F3 — Constructive and digital
Digital (107, 158, 156)-net over F3, using
- 12 times m-reduction [i] based on digital (107, 170, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 85, 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, 85, 78)-net over F9, using
(158−51, 158, 288)-Net over F3 — Digital
Digital (107, 158, 288)-net over F3, using
(158−51, 158, 5021)-Net in Base 3 — Upper bound on s
There is no (107, 158, 5022)-net in base 3, because
- 1 times m-reduction [i] would yield (107, 157, 5022)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 812 371039 566965 358411 071589 051971 950665 996387 852108 863308 598217 484923 726733 > 3157 [i]