Best Known (46, 46+61, s)-Nets in Base 2
(46, 46+61, 34)-Net over F2 — Constructive and digital
Digital (46, 107, 34)-net over F2, using
- t-expansion [i] based on digital (45, 107, 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+61, 100)-Net in Base 2 — Upper bound on s
There is no (46, 107, 101)-net in base 2, because
- 1 times m-reduction [i] would yield (46, 106, 101)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 90 678107 533901 002575 831580 715392 > 2106 [i]