Best Known (52, 52+26, s)-Nets in Base 2
(52, 52+26, 60)-Net over F2 — Constructive and digital
Digital (52, 78, 60)-net over F2, using
- trace code for nets [i] based on digital (13, 39, 30)-net over F4, using
- net from sequence [i] based on digital (13, 29)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 13 and N(F) ≥ 30, using
- F4 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) = 13 and N(F) ≥ 30, using
- net from sequence [i] based on digital (13, 29)-sequence over F4, using
(52, 52+26, 67)-Net over F2 — Digital
Digital (52, 78, 67)-net over F2, using
(52, 52+26, 344)-Net in Base 2 — Upper bound on s
There is no (52, 78, 345)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 311366 547827 863639 374824 > 278 [i]