Best Known (253−180, 253, s)-Nets in Base 2
(253−180, 253, 49)-Net over F2 — Constructive and digital
Digital (73, 253, 49)-net over F2, using
- t-expansion [i] based on digital (70, 253, 49)-net over F2, using
- net from sequence [i] based on digital (70, 48)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 69, N(F) = 48, and 1 place with degree 2 [i] based on function field F/F2 with g(F) = 69 and N(F) ≥ 48, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (70, 48)-sequence over F2, using
(253−180, 253, 106)-Net in Base 2 — Upper bound on s
There is no (73, 253, 107)-net in base 2, because
- 46 times m-reduction [i] would yield (73, 207, 107)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2207, 107, S2, 2, 134), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 6582 018229 284824 168619 876730 229402 019930 943462 534319 453394 436096 / 27 > 2207 [i]
- extracting embedded OOA [i] would yield OOA(2207, 107, S2, 2, 134), but