Best Known (109−55, 109, s)-Nets in Base 2
(109−55, 109, 42)-Net over F2 — Constructive and digital
Digital (54, 109, 42)-net over F2, using
- net from sequence [i] based on digital (54, 41)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 54 and N(F) ≥ 42, using
(109−55, 109, 119)-Net in Base 2 — Upper bound on s
There is no (54, 109, 120)-net in base 2, because
- 1 times m-reduction [i] would yield (54, 108, 120)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2108, 120, S2, 54), but
- the linear programming bound shows that M ≥ 134999 718321 905518 341792 904559 722496 / 357 > 2108 [i]
- extracting embedded orthogonal array [i] would yield OA(2108, 120, S2, 54), but