Best Known (45, 45+208, s)-Nets in Base 2
(45, 45+208, 34)-Net over F2 — Constructive and digital
Digital (45, 253, 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+208, 55)-Net in Base 2 — Upper bound on s
There is no (45, 253, 56)-net in base 2, because
- 36 times m-reduction [i] would yield (45, 217, 56)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2217, 56, S2, 4, 172), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 40 439920 000725 959692 000522 630529 446010 455716 633810 858721 655415 373824 / 173 > 2217 [i]
- extracting embedded OOA [i] would yield OOA(2217, 56, S2, 4, 172), but