Best Known (72−63, 72, s)-Nets in Base 2
(72−63, 72, 12)-Net over F2 — Constructive and digital
Digital (9, 72, 12)-net over F2, using
- net from sequence [i] based on digital (9, 11)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 9 and N(F) ≥ 12, using
(72−63, 72, 15)-Net in Base 2 — Upper bound on s
There is no (9, 72, 16)-net in base 2, because
- 14 times m-reduction [i] would yield (9, 58, 16)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(258, 16, S2, 4, 49), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 9 223372 036854 775808 / 25 > 258 [i]
- extracting embedded OOA [i] would yield OOA(258, 16, S2, 4, 49), but