Best Known (20, 20+98, s)-Nets in Base 2
(20, 20+98, 20)-Net over F2 — Constructive and digital
Digital (20, 118, 20)-net over F2, using
- t-expansion [i] based on digital (19, 118, 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
(20, 20+98, 28)-Net in Base 2 — Upper bound on s
There is no (20, 118, 29)-net in base 2, because
- 9 times m-reduction [i] would yield (20, 109, 29)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2109, 29, S2, 4, 89), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 49326 820156 080862 471039 715127 590912 / 45 > 2109 [i]
- extracting embedded OOA [i] would yield OOA(2109, 29, S2, 4, 89), but