Best Known (67, 67+142, s)-Nets in Base 2
(67, 67+142, 43)-Net over F2 — Constructive and digital
Digital (67, 209, 43)-net over F2, using
- t-expansion [i] based on digital (59, 209, 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
(67, 67+142, 48)-Net over F2 — Digital
Digital (67, 209, 48)-net over F2, using
- t-expansion [i] based on digital (65, 209, 48)-net over F2, using
- net from sequence [i] based on digital (65, 47)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 65 and N(F) ≥ 48, using
- net from sequence [i] based on digital (65, 47)-sequence over F2, using
(67, 67+142, 98)-Net in Base 2 — Upper bound on s
There is no (67, 209, 99)-net in base 2, because
- 18 times m-reduction [i] would yield (67, 191, 99)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2191, 99, S2, 2, 124), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 100433 627766 186892 221372 630771 322662 657637 687111 424552 206336 / 25 > 2191 [i]
- extracting embedded OOA [i] would yield OOA(2191, 99, S2, 2, 124), but