Best Known (33, s)-Sequences in Base 4
(33, 55)-Sequence over F4 — Constructive and digital
Digital (33, 55)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 33 and N(F) ≥ 56, using
- F5 from the tower of function fields by GarcÃa and Stichtenoth over F4 [i]
(33, 64)-Sequence over F4 — Digital
Digital (33, 64)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 33 and N(F) ≥ 65, using
(33, 111)-Sequence in Base 4 — Upper bound on s
There is no (33, 112)-sequence in base 4, because
- net from sequence [i] would yield (33, m, 113)-net in base 4 for arbitrarily large m, but
- m-reduction [i] would yield (33, 447, 113)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(4447, 113, S4, 4, 414), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 70 263172 641043 477764 861191 393896 708667 006694 362804 162443 018774 300547 629040 044406 310097 495033 058405 989991 694534 103198 114291 352225 413857 176454 321684 135570 963728 815428 971867 676194 441291 850964 716660 052222 976792 088057 751687 762935 957711 265506 787536 015851 373108 631259 399153 778688 / 415 > 4447 [i]
- extracting embedded OOA [i] would yield OOA(4447, 113, S4, 4, 414), but
- m-reduction [i] would yield (33, 447, 113)-net in base 4, but