Best Known (77, s)-Sequences in Base 4
(77, 103)-Sequence over F4 — Constructive and digital
Digital (77, 103)-sequence over F4, using
- t-expansion [i] based on digital (73, 103)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 104, using
- F6 from the tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 104, using
(77, 111)-Sequence over F4 — Digital
Digital (77, 111)-sequence over F4, using
- t-expansion [i] based on digital (73, 111)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 73 and N(F) ≥ 112, using
(77, 245)-Sequence in Base 4 — Upper bound on s
There is no (77, 246)-sequence in base 4, because
- net from sequence [i] would yield (77, m, 247)-net in base 4 for arbitrarily large m, but
- m-reduction [i] would yield (77, 983, 247)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(4983, 247, S4, 4, 906), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 6 923588 227388 260927 430908 174836 533932 522411 570906 919821 251869 873094 220219 660175 761414 570895 861255 096012 668331 188563 091175 695969 976101 334459 132426 913063 115789 935613 793469 006316 777876 065902 917557 791828 198923 366828 215876 222840 606837 128837 385621 033791 843444 200723 563335 205315 765707 720172 991331 169971 611890 048828 939848 446048 505825 692854 487628 150092 284685 725721 323793 667139 506457 652921 380753 827878 778889 258195 764650 545938 009139 765282 936079 176003 573104 308240 665909 983638 539848 398871 190161 011754 820802 972493 910613 360401 751715 229321 814999 597357 147794 462840 078771 095824 847454 068510 857793 002634 431329 992704 / 907 > 4983 [i]
- extracting embedded OOA [i] would yield OOA(4983, 247, S4, 4, 906), but
- m-reduction [i] would yield (77, 983, 247)-net in base 4, but