Best Known (125−86, 125, s)-Nets in Base 2
(125−86, 125, 33)-Net over F2 — Constructive and digital
Digital (39, 125, 33)-net over F2, using
- net from sequence [i] based on digital (39, 32)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 39 and N(F) ≥ 33, using
(125−86, 125, 60)-Net in Base 2 — Upper bound on s
There is no (39, 125, 61)-net in base 2, because
- 10 times m-reduction [i] would yield (39, 115, 61)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2115, 61, S2, 2, 76), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 3 987683 987354 747618 711421 180841 033728 / 77 > 2115 [i]
- extracting embedded OOA [i] would yield OOA(2115, 61, S2, 2, 76), but