Best Known (69−48, 69, s)-Nets in Base 2
(69−48, 69, 21)-Net over F2 — Constructive and digital
Digital (21, 69, 21)-net over F2, using
- net from sequence [i] based on digital (21, 20)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 21 and N(F) ≥ 21, using
(69−48, 69, 35)-Net in Base 2 — Upper bound on s
There is no (21, 69, 36)-net in base 2, because
- 3 times m-reduction [i] would yield (21, 66, 36)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(266, 36, S2, 2, 45), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 2361 183241 434822 606848 / 23 > 266 [i]
- extracting embedded OOA [i] would yield OOA(266, 36, S2, 2, 45), but