Best Known (82−41, 82, s)-Nets in Base 2
(82−41, 82, 33)-Net over F2 — Constructive and digital
Digital (41, 82, 33)-net over F2, using
- t-expansion [i] based on digital (39, 82, 33)-net over F2, using
- net from sequence [i] based on digital (39, 32)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 39 and N(F) ≥ 33, using
- net from sequence [i] based on digital (39, 32)-sequence over F2, using
(82−41, 82, 93)-Net over F2 — Upper bound on s (digital)
There is no digital (41, 82, 94)-net over F2, because
- 1 times m-reduction [i] would yield digital (41, 81, 94)-net over F2, but
- extracting embedded orthogonal array [i] would yield linear OA(281, 94, F2, 40) (dual of [94, 13, 41]-code), but
(82−41, 82, 95)-Net in Base 2 — Upper bound on s
There is no (41, 82, 96)-net in base 2, because
- 1 times m-reduction [i] would yield (41, 81, 96)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(281, 96, S2, 40), but
- the linear programming bound shows that M ≥ 85727 347720 512584 036764 352512 / 34125 > 281 [i]
- extracting embedded orthogonal array [i] would yield OA(281, 96, S2, 40), but