Best Known (45−24, 45, s)-Nets in Base 2
(45−24, 45, 21)-Net over F2 — Constructive and digital
Digital (21, 45, 21)-net over F2, using
- net from sequence [i] based on digital (21, 20)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 21 and N(F) ≥ 21, using
(45−24, 45, 49)-Net over F2 — Upper bound on s (digital)
There is no digital (21, 45, 50)-net over F2, because
- extracting embedded orthogonal array [i] would yield linear OA(245, 50, F2, 24) (dual of [50, 5, 25]-code), but
(45−24, 45, 52)-Net in Base 2 — Upper bound on s
There is no (21, 45, 53)-net in base 2, because
- extracting embedded orthogonal array [i] would yield OA(245, 53, S2, 24), but
- the linear programming bound shows that M ≥ 9851 624184 872960 / 247 > 245 [i]