Best Known (219−158, 219, s)-Nets in Base 2
(219−158, 219, 43)-Net over F2 — Constructive and digital
Digital (61, 219, 43)-net over F2, using
- t-expansion [i] based on digital (59, 219, 43)-net over F2, using
- net from sequence [i] based on digital (59, 42)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 54, N(F) = 42, and 1 place with degree 6 [i] based on function field F/F2 with g(F) = 54 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (59, 42)-sequence over F2, using
(219−158, 219, 90)-Net in Base 2 — Upper bound on s
There is no (61, 219, 91)-net in base 2, because
- 44 times m-reduction [i] would yield (61, 175, 91)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2175, 91, S2, 2, 114), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1 532495 540865 888858 358347 027150 309183 618739 122183 602176 / 23 > 2175 [i]
- extracting embedded OOA [i] would yield OOA(2175, 91, S2, 2, 114), but