Best Known (24, s)-Sequences in Base 7
(24, 29)-Sequence over F7 — Constructive and digital
Digital (24, 29)-sequence over F7, using
- t-expansion [i] based on digital (23, 29)-sequence over F7, using
(24, 71)-Sequence over F7 — Digital
Digital (24, 71)-sequence over F7, using
- t-expansion [i] based on digital (22, 71)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 22 and N(F) ≥ 72, using
(24, 162)-Sequence in Base 7 — Upper bound on s
There is no (24, 163)-sequence in base 7, because
- net from sequence [i] would yield (24, m, 164)-net in base 7 for arbitrarily large m, but
- m-reduction [i] would yield (24, 488, 164)-net in base 7, but
- extracting embedded OOA [i] would yield OOA(7488, 164, S7, 3, 464), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 5 192058 353724 623655 364228 210779 132497 593767 057139 289602 335871 991988 001237 325804 641110 569184 478007 428900 195562 191457 533769 290030 218361 392634 059845 292922 481543 368070 540275 965645 476760 931707 843324 569075 961447 308766 641446 127741 281251 581906 007561 014303 924442 005586 918499 840113 617881 234664 660321 984297 358069 567227 318504 072788 585884 899096 002480 339468 536073 348569 769840 522462 796802 257553 001722 403974 215444 806596 247795 118603 / 155 > 7488 [i]
- extracting embedded OOA [i] would yield OOA(7488, 164, S7, 3, 464), but
- m-reduction [i] would yield (24, 488, 164)-net in base 7, but