Best Known (62, s)-Sequences in Base 3
(62, 47)-Sequence over F3 — Constructive and digital
Digital (62, 47)-sequence over F3, using
- t-expansion [i] based on digital (45, 47)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 45 and N(F) ≥ 48, using
(62, 63)-Sequence over F3 — Digital
Digital (62, 63)-sequence over F3, using
- t-expansion [i] based on digital (49, 63)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 49 and N(F) ≥ 64, using
(62, 135)-Sequence in Base 3 — Upper bound on s
There is no (62, 136)-sequence in base 3, because
- net from sequence [i] would yield (62, m, 137)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (62, 679, 137)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3679, 137, S3, 5, 617), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 136 644976 423706 731165 934361 295523 971871 653902 721756 189897 181857 922264 321516 317764 543986 605536 140641 272641 091573 658522 417030 995111 683505 313035 918367 430568 692230 433699 415940 142545 863779 729877 697044 056779 874052 356802 076113 527791 126435 040293 367693 800243 700869 348084 417026 094543 281917 416854 464595 376856 023997 270389 292269 538867 060316 / 103 > 3679 [i]
- extracting embedded OOA [i] would yield OOA(3679, 137, S3, 5, 617), but
- m-reduction [i] would yield (62, 679, 137)-net in base 3, but