Best Known (84−68, 84, s)-Nets in Base 2
(84−68, 84, 17)-Net over F2 — Constructive and digital
Digital (16, 84, 17)-net over F2, using
- t-expansion [i] based on digital (15, 84, 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
- net from sequence [i] based on digital (15, 16)-sequence over F2, using
(84−68, 84, 24)-Net in Base 2 — Upper bound on s
There is no (16, 84, 25)-net in base 2, because
- 15 times m-reduction [i] would yield (16, 69, 25)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(269, 25, S2, 3, 53), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 16528 282690 043758 247936 / 27 > 269 [i]
- extracting embedded OOA [i] would yield OOA(269, 25, S2, 3, 53), but