Best Known (78−68, 78, s)-Nets in Base 2
(78−68, 78, 12)-Net over F2 — Constructive and digital
Digital (10, 78, 12)-net over F2, using
- t-expansion [i] based on digital (9, 78, 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
- net from sequence [i] based on digital (9, 11)-sequence over F2, using
(78−68, 78, 13)-Net over F2 — Digital
Digital (10, 78, 13)-net over F2, using
- net from sequence [i] based on digital (10, 12)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 10 and N(F) ≥ 13, using
(78−68, 78, 16)-Net in Base 2 — Upper bound on s
There is no (10, 78, 17)-net in base 2, because
- 16 times m-reduction [i] would yield (10, 62, 17)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(262, 17, S2, 4, 52), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 276 701161 105643 274240 / 53 > 262 [i]
- extracting embedded OOA [i] would yield OOA(262, 17, S2, 4, 52), but