Best Known (67, 67+38, s)-Nets in Base 2
(67, 67+38, 60)-Net over F2 — Constructive and digital
Digital (67, 105, 60)-net over F2, using
- 3 times m-reduction [i] based on digital (67, 108, 60)-net over F2, using
- trace code for nets [i] based on digital (13, 54, 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
- trace code for nets [i] based on digital (13, 54, 30)-net over F4, using
(67, 67+38, 69)-Net over F2 — Digital
Digital (67, 105, 69)-net over F2, using
(67, 67+38, 338)-Net in Base 2 — Upper bound on s
There is no (67, 105, 339)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 41 929140 143196 623771 491590 927086 > 2105 [i]