Best Known (67, 257, s)-Nets in Base 2
(67, 257, 43)-Net over F2 — Constructive and digital
Digital (67, 257, 43)-net over F2, using
- t-expansion [i] based on digital (59, 257, 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, 257, 48)-Net over F2 — Digital
Digital (67, 257, 48)-net over F2, using
- t-expansion [i] based on digital (65, 257, 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, 257, 85)-Net in Base 2 — Upper bound on s
There is no (67, 257, 86)-net in base 2, because
- 7 times m-reduction [i] would yield (67, 250, 86)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2250, 86, S2, 3, 183), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 72370 055773 322622 139731 865630 429942 408293 740416 025352 524660 990004 945706 024960 / 23 > 2250 [i]
- extracting embedded OOA [i] would yield OOA(2250, 86, S2, 3, 183), but