Best Known (34, 68, s)-Nets in Base 2
(34, 68, 24)-Net over F2 — Constructive and digital
Digital (34, 68, 24)-net over F2, using
- t-expansion [i] based on digital (33, 68, 24)-net over F2, using
- net from sequence [i] based on digital (33, 23)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 33 and N(F) ≥ 24, using
- net from sequence [i] based on digital (33, 23)-sequence over F2, using
(34, 68, 28)-Net over F2 — Digital
Digital (34, 68, 28)-net over F2, using
- t-expansion [i] based on digital (33, 68, 28)-net over F2, using
- net from sequence [i] based on digital (33, 27)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 33 and N(F) ≥ 28, using
- net from sequence [i] based on digital (33, 27)-sequence over F2, using
(34, 68, 78)-Net over F2 — Upper bound on s (digital)
There is no digital (34, 68, 79)-net over F2, because
- extracting embedded orthogonal array [i] would yield linear OA(268, 79, F2, 34) (dual of [79, 11, 35]-code), but
(34, 68, 81)-Net in Base 2 — Upper bound on s
There is no (34, 68, 82)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(268, 82, S2, 34), but
- the linear programming bound shows that M ≥ 705993 789189 011959 447552 / 2233 > 268 [i]