Best Known (64, 64+175, s)-Nets in Base 2
(64, 64+175, 43)-Net over F2 — Constructive and digital
Digital (64, 239, 43)-net over F2, using
- t-expansion [i] based on digital (59, 239, 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
(64, 64+175, 44)-Net over F2 — Digital
Digital (64, 239, 44)-net over F2, using
- t-expansion [i] based on digital (62, 239, 44)-net over F2, using
- net from sequence [i] based on digital (62, 43)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 62 and N(F) ≥ 44, using
- net from sequence [i] based on digital (62, 43)-sequence over F2, using
(64, 64+175, 81)-Net in Base 2 — Upper bound on s
There is no (64, 239, 82)-net in base 2, because
- 1 times m-reduction [i] would yield (64, 238, 82)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2238, 82, S2, 3, 174), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 84 808659 109362 447819 998280 035660 088759 719227 050029 709989 837097 662045 749248 / 175 > 2238 [i]
- extracting embedded OOA [i] would yield OOA(2238, 82, S2, 3, 174), but