Best Known (109−108, 109, s)-Nets in Base 2
(109−108, 109, 5)-Net over F2 — Constructive and digital
Digital (1, 109, 5)-net over F2, using
- net from sequence [i] based on digital (1, 4)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 1 and N(F) ≥ 5, using
(109−108, 109, 5)-Net in Base 2 — Upper bound on s
There is no (1, 109, 6)-net in base 2, because
- 102 times m-reduction [i] would yield (1, 7, 6)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 138 > 27 [i]