Best Known (129, 129+63, s)-Nets in Base 2
(129, 129+63, 112)-Net over F2 — Constructive and digital
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
(129, 129+63, 140)-Net over F2 — Digital
Digital (129, 192, 140)-net over F2, using
(129, 129+63, 843)-Net in Base 2 — Upper bound on s
There is no (129, 192, 844)-net in base 2, because
- 1 times m-reduction [i] would yield (129, 191, 844)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 3162 592774 475034 059535 663595 586796 239774 408780 919926 650800 > 2191 [i]