Best Known (87−68, 87, s)-Nets in Base 2
(87−68, 87, 20)-Net over F2 — Constructive and digital
Digital (19, 87, 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
(87−68, 87, 28)-Net in Base 2 — Upper bound on s
There is no (19, 87, 29)-net in base 2, because
- 6 times m-reduction [i] would yield (19, 81, 29)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(281, 29, S2, 3, 62), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 212 770944 252174 734748 286976 / 63 > 281 [i]
- extracting embedded OOA [i] would yield OOA(281, 29, S2, 3, 62), but