Best Known (129, 129+56, s)-Nets in Base 2
(129, 129+56, 112)-Net over F2 — Constructive and digital
Digital (129, 185, 112)-net over F2, using
- 7 times m-reduction [i] based on digital (129, 192, 112)-net over F2, using
- trace code for nets [i] based on digital (33, 96, 56)-net over F4, using
- net from sequence [i] based on digital (33, 55)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 33 and N(F) ≥ 56, using
- F5 from the tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 33 and N(F) ≥ 56, using
- net from sequence [i] based on digital (33, 55)-sequence over F4, using
- trace code for nets [i] based on digital (33, 96, 56)-net over F4, using
(129, 129+56, 164)-Net over F2 — Digital
Digital (129, 185, 164)-net over F2, using
(129, 129+56, 1060)-Net in Base 2 — Upper bound on s
There is no (129, 185, 1061)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 49 514793 551796 964505 846060 679690 368368 258782 972141 235572 > 2185 [i]