Best Known (46, 46+∞, s)-Nets in Base 2
(46, 46+∞, 34)-Net over F2 — Constructive and digital
Digital (46, m, 34)-net over F2 for arbitrarily large m, using
- net from sequence [i] based on digital (46, 33)-sequence over F2, using
- t-expansion [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]
- t-expansion [i] based on digital (45, 33)-sequence over F2, using
(46, 46+∞, 54)-Net in Base 2 — Upper bound on s
There is no (46, m, 55)-net in base 2 for arbitrarily large m, because
- m-reduction [i] would yield (46, 322, 55)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2322, 55, S2, 6, 276), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 2494 832857 955622 976237 385352 806036 869855 958882 112570 435298 144597 936352 639711 788162 426819 717541 920768 / 277 > 2322 [i]
- extracting embedded OOA [i] would yield OOA(2322, 55, S2, 6, 276), but