Best Known (156, 156+82, s)-Nets in Base 3
(156, 156+82, 162)-Net over F3 — Constructive and digital
Digital (156, 238, 162)-net over F3, using
- 10 times m-reduction [i] based on digital (156, 248, 162)-net over F3, using
- trace code for nets [i] based on digital (32, 124, 81)-net over F9, using
- net from sequence [i] based on digital (32, 80)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- F4 from the tower of function fields by Bezerra and GarcÃa over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- net from sequence [i] based on digital (32, 80)-sequence over F9, using
- trace code for nets [i] based on digital (32, 124, 81)-net over F9, using
(156, 156+82, 335)-Net over F3 — Digital
Digital (156, 238, 335)-net over F3, using
(156, 156+82, 4707)-Net in Base 3 — Upper bound on s
There is no (156, 238, 4708)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 359812 883752 346568 570043 903125 005847 950516 195853 623878 774550 521432 700018 426855 444927 416844 564066 690509 062038 107593 > 3238 [i]