Best Known (69−54, 69, s)-Nets in Base 2
(69−54, 69, 17)-Net over F2 — Constructive and digital
Digital (15, 69, 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
(69−54, 69, 23)-Net in Base 2 — Upper bound on s
There is no (15, 69, 24)-net in base 2, because
- 3 times m-reduction [i] would yield (15, 66, 24)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(266, 24, S2, 3, 51), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1180 591620 717411 303424 / 13 > 266 [i]
- extracting embedded OOA [i] would yield OOA(266, 24, S2, 3, 51), but