Best Known (111−90, 111, s)-Nets in Base 2
(111−90, 111, 21)-Net over F2 — Constructive and digital
Digital (21, 111, 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
(111−90, 111, 30)-Net in Base 2 — Upper bound on s
There is no (21, 111, 31)-net in base 2, because
- 24 times m-reduction [i] would yield (21, 87, 31)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(287, 31, S2, 3, 66), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 11141 460353 568422 474092 118016 / 67 > 287 [i]
- extracting embedded OOA [i] would yield OOA(287, 31, S2, 3, 66), but