Best Known (218−76, 218, s)-Nets in Base 2
(218−76, 218, 112)-Net over F2 — Constructive and digital
Digital (142, 218, 112)-net over F2, using
- trace code for nets [i] based on digital (33, 109, 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
(218−76, 218, 136)-Net over F2 — Digital
Digital (142, 218, 136)-net over F2, using
(218−76, 218, 746)-Net in Base 2 — Upper bound on s
There is no (142, 218, 747)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 431374 270707 794873 763400 642837 062171 835682 528655 143961 597012 577110 > 2218 [i]