Best Known (19, 19+54, s)-Nets in Base 2
(19, 19+54, 20)-Net over F2 — Constructive and digital
Digital (19, 73, 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+54, 32)-Net in Base 2 — Upper bound on s
There is no (19, 73, 33)-net in base 2, because
- 13 times m-reduction [i] would yield (19, 60, 33)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(260, 33, S2, 2, 41), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 9 223372 036854 775808 / 7 > 260 [i]
- extracting embedded OOA [i] would yield OOA(260, 33, S2, 2, 41), but