Best Known (135, 135+86, s)-Nets in Base 3
(135, 135+86, 156)-Net over F3 — Constructive and digital
Digital (135, 221, 156)-net over F3, using
- 5 times m-reduction [i] based on digital (135, 226, 156)-net over F3, using
- trace code for nets [i] based on digital (22, 113, 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, 113, 78)-net over F9, using
(135, 135+86, 220)-Net over F3 — Digital
Digital (135, 221, 220)-net over F3, using
(135, 135+86, 2349)-Net in Base 3 — Upper bound on s
There is no (135, 221, 2350)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 2827 095266 395330 207395 493100 230729 029339 349505 391025 804301 924785 034220 347761 965579 052043 978112 259031 826609 > 3221 [i]