Best Known (94, s)-Sequences in Base 2
(94, 52)-Sequence over F2 — Constructive and digital
Digital (94, 52)-sequence over F2, using
- t-expansion [i] based on digital (90, 52)-sequence over F2, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F2 with g(F) = 69, N(F) = 48, 1 place with degree 2, and 4 places with degree 6 [i] based on function field F/F2 with g(F) = 69 and N(F) ≥ 48, using an explicitly constructive algebraic function field [i]
(94, 59)-Sequence over F2 — Digital
Digital (94, 59)-sequence over F2, using
- t-expansion [i] based on digital (92, 59)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 92 and N(F) ≥ 60, using
(94, 102)-Sequence in Base 2 — Upper bound on s
There is no (94, 103)-sequence in base 2, because
- net from sequence [i] would yield (94, m, 104)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (94, 823, 104)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2823, 104, S2, 8, 729), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 22821 626560 034734 709771 218447 147136 922293 885902 823488 734398 655231 529129 129265 595501 978273 399329 000736 670270 858908 890401 934284 998415 792847 058167 130126 871774 385096 196714 170934 643993 857255 241061 212320 266256 559671 994082 382159 905369 011943 489033 475471 704064 / 365 > 2823 [i]
- extracting embedded OOA [i] would yield OOA(2823, 104, S2, 8, 729), but
- m-reduction [i] would yield (94, 823, 104)-net in base 2, but