Best Known (212−154, 212, s)-Nets in Base 2
(212−154, 212, 42)-Net over F2 — Constructive and digital
Digital (58, 212, 42)-net over F2, using
- t-expansion [i] based on digital (54, 212, 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
- net from sequence [i] based on digital (54, 41)-sequence over F2, using
(212−154, 212, 86)-Net in Base 2 — Upper bound on s
There is no (58, 212, 87)-net in base 2, because
- 45 times m-reduction [i] would yield (58, 167, 87)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2167, 87, S2, 2, 109), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 2993 155353 253689 176481 146537 402947 624255 349848 014848 / 11 > 2167 [i]
- extracting embedded OOA [i] would yield OOA(2167, 87, S2, 2, 109), but