Best Known (129, 129+62, s)-Nets in Base 3
(129, 129+62, 162)-Net over F3 — Constructive and digital
Digital (129, 191, 162)-net over F3, using
- 3 times m-reduction [i] based on digital (129, 194, 162)-net over F3, using
- trace code for nets [i] based on digital (32, 97, 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, 97, 81)-net over F9, using
(129, 129+62, 333)-Net over F3 — Digital
Digital (129, 191, 333)-net over F3, using
(129, 129+62, 5373)-Net in Base 3 — Upper bound on s
There is no (129, 191, 5374)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 13 556595 417508 175532 034504 954374 842106 487609 560964 126300 107547 749829 341842 507721 236128 670409 > 3191 [i]