Best Known (126−93, 126, s)-Nets in Base 2
(126−93, 126, 24)-Net over F2 — Constructive and digital
Digital (33, 126, 24)-net over F2, using
- net from sequence [i] based on digital (33, 23)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 33 and N(F) ≥ 24, using
(126−93, 126, 28)-Net over F2 — Digital
Digital (33, 126, 28)-net over F2, using
- net from sequence [i] based on digital (33, 27)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 33 and N(F) ≥ 28, using
(126−93, 126, 52)-Net in Base 2 — Upper bound on s
There is no (33, 126, 53)-net in base 2, because
- 27 times m-reduction [i] would yield (33, 99, 53)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(299, 53, S2, 2, 66), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 60 847228 810955 011271 841753 858048 / 67 > 299 [i]
- extracting embedded OOA [i] would yield OOA(299, 53, S2, 2, 66), but