Best Known (231−170, 231, s)-Nets in Base 2
(231−170, 231, 43)-Net over F2 — Constructive and digital
Digital (61, 231, 43)-net over F2, using
- t-expansion [i] based on digital (59, 231, 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
(231−170, 231, 78)-Net in Base 2 — Upper bound on s
There is no (61, 231, 79)-net in base 2, because
- 2 times m-reduction [i] would yield (61, 229, 79)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2229, 79, S2, 3, 168), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 248462 868484 460296 347651 211041 972916 288239 922998 133915 985850 872056 774656 / 169 > 2229 [i]
- extracting embedded OOA [i] would yield OOA(2229, 79, S2, 3, 168), but