Best Known (119−59, 119, s)-Nets in Base 2
(119−59, 119, 43)-Net over F2 — Constructive and digital
Digital (60, 119, 43)-net over F2, using
- t-expansion [i] based on digital (59, 119, 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
(119−59, 119, 133)-Net in Base 2 — Upper bound on s
There is no (60, 119, 134)-net in base 2, because
- 1 times m-reduction [i] would yield (60, 118, 134)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2118, 134, S2, 58), but
- the linear programming bound shows that M ≥ 10548 753374 549092 367364 612830 384814 555136 / 30135 > 2118 [i]
- extracting embedded orthogonal array [i] would yield OA(2118, 134, S2, 58), but