Best Known (212−166, 212, s)-Nets in Base 2
(212−166, 212, 34)-Net over F2 — Constructive and digital
Digital (46, 212, 34)-net over F2, using
- t-expansion [i] based on digital (45, 212, 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
(212−166, 212, 60)-Net in Base 2 — Upper bound on s
There is no (46, 212, 61)-net in base 2, because
- 36 times m-reduction [i] would yield (46, 176, 61)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2176, 61, S2, 3, 130), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 16 857450 949524 777441 941817 298653 401019 806130 344019 623936 / 131 > 2176 [i]
- extracting embedded OOA [i] would yield OOA(2176, 61, S2, 3, 130), but