Best Known (231−177, 231, s)-Nets in Base 2
(231−177, 231, 42)-Net over F2 — Constructive and digital
Digital (54, 231, 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
(231−177, 231, 69)-Net in Base 2 — Upper bound on s
There is no (54, 231, 70)-net in base 2, because
- 28 times m-reduction [i] would yield (54, 203, 70)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2203, 70, S2, 3, 149), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 205 688069 665150 755269 371147 819668 813122 841983 204197 482918 576128 / 15 > 2203 [i]
- extracting embedded OOA [i] would yield OOA(2203, 70, S2, 3, 149), but