Best Known (35, 35+53, s)-Nets in Base 2
(35, 35+53, 24)-Net over F2 — Constructive and digital
Digital (35, 88, 24)-net over F2, using
- t-expansion [i] based on digital (33, 88, 24)-net over F2, using
- net from sequence [i] based on digital (33, 23)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 33 and N(F) ≥ 24, using
- net from sequence [i] based on digital (33, 23)-sequence over F2, using
(35, 35+53, 29)-Net over F2 — Digital
Digital (35, 88, 29)-net over F2, using
- net from sequence [i] based on digital (35, 28)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 35 and N(F) ≥ 29, using
(35, 35+53, 74)-Net in Base 2 — Upper bound on s
There is no (35, 88, 75)-net in base 2, because
- 1 times m-reduction [i] would yield (35, 87, 75)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 193 977021 758529 206722 981204 > 287 [i]