Best Known (231−185, 231, s)-Nets in Base 2
(231−185, 231, 34)-Net over F2 — Constructive and digital
Digital (46, 231, 34)-net over F2, using
- t-expansion [i] based on digital (45, 231, 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
(231−185, 231, 56)-Net in Base 2 — Upper bound on s
There is no (46, 231, 57)-net in base 2, because
- 10 times m-reduction [i] would yield (46, 221, 57)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2221, 57, S2, 4, 175), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 38 754923 334029 044704 833834 187590 719093 353395 107402 072941 586439 733248 / 11 > 2221 [i]
- extracting embedded OOA [i] would yield OOA(2221, 57, S2, 4, 175), but