Best Known (69, 69+119, s)-Nets in Base 2
(69, 69+119, 48)-Net over F2 — Constructive and digital
Digital (69, 188, 48)-net over F2, using
- net from sequence [i] based on digital (69, 47)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 69 and N(F) ≥ 48, using
(69, 69+119, 49)-Net over F2 — Digital
Digital (69, 188, 49)-net over F2, using
- t-expansion [i] based on digital (68, 188, 49)-net over F2, using
- net from sequence [i] based on digital (68, 48)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 68 and N(F) ≥ 49, using
- net from sequence [i] based on digital (68, 48)-sequence over F2, using
(69, 69+119, 131)-Net in Base 2 — Upper bound on s
There is no (69, 188, 132)-net in base 2, because
- 1 times m-reduction [i] would yield (69, 187, 132)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 233 289017 628485 296384 786995 797346 876988 906482 933125 103216 > 2187 [i]