Best Known (19, 19+25, s)-Nets in Base 2
(19, 19+25, 20)-Net over F2 — Constructive and digital
Digital (19, 44, 20)-net over F2, using
- net from sequence [i] based on digital (19, 19)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 19 and N(F) ≥ 20, using
(19, 19+25, 46)-Net in Base 2 — Upper bound on s
There is no (19, 44, 47)-net in base 2, because
- 1 times m-reduction [i] would yield (19, 43, 47)-net in base 2, but
- extracting embedded orthogonal array [i] would yield OA(243, 47, S2, 24), but
- adding a parity check bit [i] would yield OA(244, 48, S2, 25), but
- the (dual) Plotkin bound shows that M ≥ 281 474976 710656 / 13 > 244 [i]
- adding a parity check bit [i] would yield OA(244, 48, S2, 25), but
- extracting embedded orthogonal array [i] would yield OA(243, 47, S2, 24), but