Best Known (73−39, 73, s)-Nets in Base 2
(73−39, 73, 24)-Net over F2 — Constructive and digital
Digital (34, 73, 24)-net over F2, using
- t-expansion [i] based on digital (33, 73, 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
(73−39, 73, 28)-Net over F2 — Digital
Digital (34, 73, 28)-net over F2, using
- t-expansion [i] based on digital (33, 73, 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
(73−39, 73, 76)-Net over F2 — Upper bound on s (digital)
There is no digital (34, 73, 77)-net over F2, because
- 3 times m-reduction [i] would yield digital (34, 70, 77)-net over F2, but
- extracting embedded orthogonal array [i] would yield linear OA(270, 77, F2, 36) (dual of [77, 7, 37]-code), but
- residual code [i] would yield linear OA(234, 40, F2, 18) (dual of [40, 6, 19]-code), but
- extracting embedded orthogonal array [i] would yield linear OA(270, 77, F2, 36) (dual of [77, 7, 37]-code), but
(73−39, 73, 79)-Net in Base 2 — Upper bound on s
There is no (34, 73, 80)-net in base 2, because
- 3 times m-reduction [i] would yield (34, 70, 80)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(270, 80, S2, 36), but
- the linear programming bound shows that M ≥ 689465 506498 968201 199616 / 437 > 270 [i]
- extracting embedded orthogonal array [i] would yield OA(270, 80, S2, 36), but