Best Known (109, s)-Sequences in Base 2
(109, 55)-Sequence over F2 — Constructive and digital
Digital (109, 55)-sequence over F2, using
- t-expansion [i] based on digital (105, 55)-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 7 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]
(109, 64)-Sequence over F2 — Digital
Digital (109, 64)-sequence over F2, using
- t-expansion [i] based on digital (95, 64)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 95 and N(F) ≥ 65, using
(109, 118)-Sequence in Base 2 — Upper bound on s
There is no (109, 119)-sequence in base 2, because
- net from sequence [i] would yield (109, m, 120)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (109, 830, 120)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2830, 120, S2, 7, 721), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 3 894890 932912 594723 800954 614979 778034 738156 527415 208744 004037 159514 304704 727994 965670 958660 152149 459058 392893 253783 961930 117973 062961 979231 260523 541652 782828 389750 905885 172845 908284 971561 141113 569325 441119 517353 656726 555290 516311 371688 795046 480504 160256 / 361 > 2830 [i]
- extracting embedded OOA [i] would yield OOA(2830, 120, S2, 7, 721), but
- m-reduction [i] would yield (109, 830, 120)-net in base 2, but