Best Known (227−167, 227, s)-Nets in Base 2
(227−167, 227, 43)-Net over F2 — Constructive and digital
Digital (60, 227, 43)-net over F2, using
- t-expansion [i] based on digital (59, 227, 43)-net over F2, using
- net from sequence [i] based on digital (59, 42)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 54, N(F) = 42, and 1 place with degree 6 [i] based on function field F/F2 with g(F) = 54 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (59, 42)-sequence over F2, using
(227−167, 227, 76)-Net in Base 2 — Upper bound on s
There is no (60, 227, 77)-net in base 2, because
- 3 times m-reduction [i] would yield (60, 224, 77)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2224, 77, S2, 3, 164), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 431 359146 674410 236714 672241 392314 090778 194310 760649 159697 657763 987456 / 15 > 2224 [i]
- extracting embedded OOA [i] would yield OOA(2224, 77, S2, 3, 164), but