Best Known (45, 45+69, s)-Nets in Base 2
(45, 45+69, 34)-Net over F2 — Constructive and digital
Digital (45, 114, 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]
(45, 45+69, 92)-Net in Base 2 — Upper bound on s
There is no (45, 114, 93)-net in base 2, because
- 1 times m-reduction [i] would yield (45, 113, 93)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 12812 788228 581861 449074 201943 074220 > 2113 [i]