Best Known (128, 128+56, s)-Nets in Base 2
(128, 128+56, 112)-Net over F2 — Constructive and digital
Digital (128, 184, 112)-net over F2, using
- 6 times m-reduction [i] based on digital (128, 190, 112)-net over F2, using
- trace code for nets [i] based on digital (33, 95, 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, 95, 56)-net over F4, using
(128, 128+56, 161)-Net over F2 — Digital
Digital (128, 184, 161)-net over F2, using
(128, 128+56, 1033)-Net in Base 2 — Upper bound on s
There is no (128, 184, 1034)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 24 707971 783759 562033 117098 242855 821864 803825 359188 116224 > 2184 [i]