Best Known (46, 46+42, s)-Nets in Base 2
(46, 46+42, 34)-Net over F2 — Constructive and digital
Digital (46, 88, 34)-net over F2, using
- t-expansion [i] based on digital (45, 88, 34)-net over F2, using
- net from sequence [i] based on digital (45, 33)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 41, N(F) = 32, 1 place with degree 2, and 1 place with degree 4 [i] based on function field F/F2 with g(F) = 41 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (45, 33)-sequence over F2, using
(46, 46+42, 111)-Net in Base 2 — Upper bound on s
There is no (46, 88, 112)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(288, 112, S2, 42), but
- the linear programming bound shows that M ≥ 99575 816509 746504 699499 485065 117696 / 317 235555 > 288 [i]