Best Known (124, 124+58, s)-Nets in Base 2
(124, 124+58, 112)-Net over F2 — Constructive and digital
Digital (124, 182, 112)-net over F2, using
- trace code for nets [i] based on digital (33, 91, 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
(124, 124+58, 143)-Net over F2 — Digital
Digital (124, 182, 143)-net over F2, using
(124, 124+58, 862)-Net in Base 2 — Upper bound on s
There is no (124, 182, 863)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 6 273627 146814 634778 117833 965952 817329 169747 495870 143404 > 2182 [i]