Best Known (134, 134+78, s)-Nets in Base 3
(134, 134+78, 156)-Net over F3 — Constructive and digital
Digital (134, 212, 156)-net over F3, using
- 12 times m-reduction [i] based on digital (134, 224, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 112, 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, 112, 78)-net over F9, using
(134, 134+78, 250)-Net over F3 — Digital
Digital (134, 212, 250)-net over F3, using
(134, 134+78, 2981)-Net in Base 3 — Upper bound on s
There is no (134, 212, 2982)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 142075 242138 320408 213676 091635 423471 517153 544074 131889 265229 499478 256773 246856 863172 503905 390409 648217 > 3212 [i]