Best Known (15, 15+48, s)-Nets in Base 2
(15, 15+48, 17)-Net over F2 — Constructive and digital
Digital (15, 63, 17)-net over F2, using
- net from sequence [i] based on digital (15, 16)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 15 and N(F) ≥ 17, using
(15, 15+48, 26)-Net in Base 2 — Upper bound on s
There is no (15, 63, 27)-net in base 2, because
- 14 times m-reduction [i] would yield (15, 49, 27)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(249, 27, S2, 2, 34), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 4503 599627 370496 / 7 > 249 [i]
- extracting embedded OOA [i] would yield OOA(249, 27, S2, 2, 34), but