Best Known (56, 56+49, s)-Nets in Base 2
(56, 56+49, 42)-Net over F2 — Constructive and digital
Digital (56, 105, 42)-net over F2, using
- t-expansion [i] based on digital (54, 105, 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
- net from sequence [i] based on digital (54, 41)-sequence over F2, using
(56, 56+49, 139)-Net in Base 2 — Upper bound on s
There is no (56, 105, 140)-net in base 2, because
- 1 times m-reduction [i] would yield (56, 104, 140)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2104, 140, S2, 48), but
- the linear programming bound shows that M ≥ 906615 640616 170781 657520 759485 197602 258944 / 38102 739675 > 2104 [i]
- extracting embedded orthogonal array [i] would yield OA(2104, 140, S2, 48), but