Best Known (21, 21+113, s)-Nets in Base 2
(21, 21+113, 21)-Net over F2 — Constructive and digital
Digital (21, 134, 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
(21, 21+113, 29)-Net in Base 2 — Upper bound on s
There is no (21, 134, 30)-net in base 2, because
- 21 times m-reduction [i] would yield (21, 113, 30)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2113, 30, S2, 4, 92), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 498460 498419 343452 338927 647605 129216 / 31 > 2113 [i]
- extracting embedded OOA [i] would yield OOA(2113, 30, S2, 4, 92), but