Best Known (189−135, 189, s)-Nets in Base 2
(189−135, 189, 42)-Net over F2 — Constructive and digital
Digital (54, 189, 42)-net over F2, using
- net from sequence [i] based on digital (54, 41)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 54 and N(F) ≥ 42, using
(189−135, 189, 80)-Net in Base 2 — Upper bound on s
There is no (54, 189, 81)-net in base 2, because
- 33 times m-reduction [i] would yield (54, 156, 81)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2156, 81, S2, 2, 102), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 10 230511 461316 320427 425793 829013 981137 591527 800832 / 103 > 2156 [i]
- extracting embedded OOA [i] would yield OOA(2156, 81, S2, 2, 102), but