Best Known (80, s)-Sequences in Base 2
(80, 50)-Sequence over F2 — Constructive and digital
Digital (80, 50)-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 2 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]
(80, 55)-Sequence over F2 — Digital
Digital (80, 55)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 80 and N(F) ≥ 56, using
(80, 88)-Sequence in Base 2 — Upper bound on s
There is no (80, 89)-sequence in base 2, because
- net from sequence [i] would yield (80, m, 90)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (80, 621, 90)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2621, 90, S2, 7, 541), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 2889 118738 270890 832116 830774 483674 468735 793808 758777 421860 297996 411436 759020 387444 152761 561121 687516 644495 481068 484007 314965 534148 209849 196281 211010 261106 701850 246871 733871 390204 456771 518464 / 271 > 2621 [i]
- extracting embedded OOA [i] would yield OOA(2621, 90, S2, 7, 541), but
- m-reduction [i] would yield (80, 621, 90)-net in base 2, but