Best Known (126−84, 126, s)-Nets in Base 2
(126−84, 126, 33)-Net over F2 — Constructive and digital
Digital (42, 126, 33)-net over F2, using
- t-expansion [i] based on digital (39, 126, 33)-net over F2, using
- net from sequence [i] based on digital (39, 32)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 39 and N(F) ≥ 33, using
- net from sequence [i] based on digital (39, 32)-sequence over F2, using
(126−84, 126, 64)-Net in Base 2 — Upper bound on s
There is no (42, 126, 65)-net in base 2, because
- 3 times m-reduction [i] would yield (42, 123, 65)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2123, 65, S2, 2, 81), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 510 423550 381407 695195 061911 147652 317184 / 41 > 2123 [i]
- extracting embedded OOA [i] would yield OOA(2123, 65, S2, 2, 81), but