Best Known (127, 179, s)-Nets in Base 2
(127, 179, 112)-Net over F2 — Constructive and digital
Digital (127, 179, 112)-net over F2, using
- 9 times m-reduction [i] based on digital (127, 188, 112)-net over F2, using
- trace code for nets [i] based on digital (33, 94, 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, 94, 56)-net over F4, using
(127, 179, 176)-Net over F2 — Digital
Digital (127, 179, 176)-net over F2, using
(127, 179, 1208)-Net in Base 2 — Upper bound on s
There is no (127, 179, 1209)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 770193 967597 668268 388807 054737 022177 673594 492756 930700 > 2179 [i]