Best Known (10, 10+46, s)-Nets in Base 2
(10, 10+46, 12)-Net over F2 — Constructive and digital
Digital (10, 56, 12)-net over F2, using
- t-expansion [i] based on digital (9, 56, 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
(10, 10+46, 13)-Net over F2 — Digital
Digital (10, 56, 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
(10, 10+46, 17)-Net in Base 2 — Upper bound on s
There is no (10, 56, 18)-net in base 2, because
- 8 times m-reduction [i] would yield (10, 48, 18)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(248, 18, S2, 3, 38), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 4503 599627 370496 / 13 > 248 [i]
- extracting embedded OOA [i] would yield OOA(248, 18, S2, 3, 38), but