Best Known (88−68, 88, s)-Nets in Base 2
(88−68, 88, 20)-Net over F2 — Constructive and digital
Digital (20, 88, 20)-net over F2, using
- t-expansion [i] based on digital (19, 88, 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
- net from sequence [i] based on digital (19, 19)-sequence over F2, using
(88−68, 88, 29)-Net in Base 2 — Upper bound on s
There is no (20, 88, 30)-net in base 2, because
- 4 times m-reduction [i] would yield (20, 84, 30)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(284, 30, S2, 3, 64), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 309 485009 821345 068724 781056 / 13 > 284 [i]
- extracting embedded OOA [i] would yield OOA(284, 30, S2, 3, 64), but