Best Known (73−61, 73, s)-Nets in Base 2
(73−61, 73, 14)-Net over F2 — Constructive and digital
Digital (12, 73, 14)-net over F2, using
- t-expansion [i] based on digital (11, 73, 14)-net over F2, using
- net from sequence [i] based on digital (11, 13)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 11 and N(F) ≥ 14, using
- net from sequence [i] based on digital (11, 13)-sequence over F2, using
(73−61, 73, 19)-Net in Base 2 — Upper bound on s
There is no (12, 73, 20)-net in base 2, because
- 18 times m-reduction [i] would yield (12, 55, 20)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(255, 20, S2, 3, 43), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 432345 564227 567616 / 11 > 255 [i]
- extracting embedded OOA [i] would yield OOA(255, 20, S2, 3, 43), but