Best Known (67, s)-Sequences in Base 5
(67, 81)-Sequence over F5 — Constructive and digital
Digital (67, 81)-sequence over F5, using
- t-expansion [i] based on digital (48, 81)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 48 and N(F) ≥ 82, using
(67, 131)-Sequence over F5 — Digital
Digital (67, 131)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 67 and N(F) ≥ 132, using
(67, 284)-Sequence in Base 5 — Upper bound on s
There is no (67, 285)-sequence in base 5, because
- net from sequence [i] would yield (67, m, 286)-net in base 5 for arbitrarily large m, but
- m-reduction [i] would yield (67, 1139, 286)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(51139, 286, S5, 4, 1072), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 16 136969 777967 441630 428627 365217 258496 645095 354641 147060 437978 610092 769607 631776 808780 597334 645099 652897 683858 044570 501520 323828 293282 436874 054242 188330 538213 496191 001534 184178 034260 191628 515943 315324 696702 273628 337057 999849 861695 348718 571124 970703 993251 567899 648596 454074 790167 168710 988637 841581 397401 633751 183959 826272 307653 379755 257945 653112 090949 807357 895153 000347 668879 596304 569796 722851 075395 666715 086595 744302 485935 017769 749063 184457 730899 786077 094441 883804 762858 185051 737393 136752 860789 893161 107595 692000 477634 648059 653772 949149 084746 060778 037916 715468 612526 182062 472461 710460 096479 685372 568976 073394 887470 782613 922004 174551 010345 599594 938668 126633 969629 262601 721053 387130 453151 112176 052126 700560 492659 464707 985285 706867 793449 572826 046205 381247 903979 692603 915196 968955 569900 572299 957275 390625 / 1073 > 51139 [i]
- extracting embedded OOA [i] would yield OOA(51139, 286, S5, 4, 1072), but
- m-reduction [i] would yield (67, 1139, 286)-net in base 5, but