Best Known (68−27, 68, s)-Nets in Base 2
(68−27, 68, 42)-Net over F2 — Constructive and digital
Digital (41, 68, 42)-net over F2, using
- trace code for nets [i] based on digital (7, 34, 21)-net over F4, using
- net from sequence [i] based on digital (7, 20)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 7 and N(F) ≥ 21, using
- net from sequence [i] based on digital (7, 20)-sequence over F4, using
(68−27, 68, 183)-Net in Base 2 — Upper bound on s
There is no (41, 68, 184)-net in base 2, because
- 1 times m-reduction [i] would yield (41, 67, 184)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 151 980415 410067 319754 > 267 [i]