Best Known (221−66, 221, s)-Nets in Base 2
(221−66, 221, 112)-Net over F2 — Constructive and digital
Digital (155, 221, 112)-net over F2, using
- 23 times m-reduction [i] based on digital (155, 244, 112)-net over F2, using
- trace code for nets [i] based on digital (33, 122, 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, 122, 56)-net over F4, using
(221−66, 221, 196)-Net over F2 — Digital
Digital (155, 221, 196)-net over F2, using
(221−66, 221, 1317)-Net in Base 2 — Upper bound on s
There is no (155, 221, 1318)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 3 415064 538055 350372 870917 649967 977761 516005 435602 341309 048015 890615 > 2221 [i]