Best Known (122−62, 122, s)-Nets in Base 2
(122−62, 122, 43)-Net over F2 — Constructive and digital
Digital (60, 122, 43)-net over F2, using
- t-expansion [i] based on digital (59, 122, 43)-net over F2, using
- net from sequence [i] based on digital (59, 42)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 54, N(F) = 42, and 1 place with degree 6 [i] based on function field F/F2 with g(F) = 54 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (59, 42)-sequence over F2, using
(122−62, 122, 131)-Net in Base 2 — Upper bound on s
There is no (60, 122, 132)-net in base 2, because
- 2 times m-reduction [i] would yield (60, 120, 132)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2120, 132, S2, 60), but
- the linear programming bound shows that M ≥ 16503 694795 665515 477973 668460 440758 255616 / 10323 > 2120 [i]
- extracting embedded orthogonal array [i] would yield OA(2120, 132, S2, 60), but