Best Known (122−65, 122, s)-Nets in Base 2
(122−65, 122, 42)-Net over F2 — Constructive and digital
Digital (57, 122, 42)-net over F2, using
- t-expansion [i] based on digital (54, 122, 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
(122−65, 122, 125)-Net in Base 2 — Upper bound on s
There is no (57, 122, 126)-net in base 2, because
- 7 times m-reduction [i] would yield (57, 115, 126)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2115, 126, S2, 58), but
- the linear programming bound shows that M ≥ 76 098302 758686 433723 742954 201049 726976 / 1575 > 2115 [i]
- extracting embedded orthogonal array [i] would yield OA(2115, 126, S2, 58), but