Best Known (67, 67+67, s)-Nets in Base 2
(67, 67+67, 43)-Net over F2 — Constructive and digital
Digital (67, 134, 43)-net over F2, using
- t-expansion [i] based on digital (59, 134, 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+67, 48)-Net over F2 — Digital
Digital (67, 134, 48)-net over F2, using
- t-expansion [i] based on digital (65, 134, 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+67, 147)-Net in Base 2 — Upper bound on s
There is no (67, 134, 148)-net in base 2, because
- 3 times m-reduction [i] would yield (67, 131, 148)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(2131, 148, S2, 64), but
- the linear programming bound shows that M ≥ 37846 106847 625102 676119 046386 674320 128891 420672 / 12 104235 > 2131 [i]
- extracting embedded orthogonal array [i] would yield OA(2131, 148, S2, 64), but