Best Known (142, s)-Sequences in Base 3
(142, 78)-Sequence over F3 — Constructive and digital
Digital (142, 78)-sequence over F3, using
- base reduction for sequences [i] based on digital (32, 78)-sequence over F9, using
- s-reduction based on digital (32, 80)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- F4 from the tower of function fields by Bezerra and GarcÃa over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- s-reduction based on digital (32, 80)-sequence over F9, using
(142, 119)-Sequence over F3 — Digital
Digital (142, 119)-sequence over F3, using
- t-expansion [i] based on digital (113, 119)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 113 and N(F) ≥ 120, using
(142, 296)-Sequence in Base 3 — Upper bound on s
There is no (142, 297)-sequence in base 3, because
- net from sequence [i] would yield (142, m, 298)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (142, 1781, 298)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(31781, 298, S3, 6, 1639), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 492576 749300 035990 979665 049611 551672 353772 204766 794039 411924 684689 894059 484398 520020 764819 366041 044657 555013 200287 208838 271605 123212 110469 017151 394747 553832 905576 201796 155182 290972 493924 549695 526909 816534 957330 416215 553972 648993 224898 873613 836171 786554 709236 331425 932627 819068 472800 731472 291434 365369 762992 697909 697441 652847 427472 777265 189608 314166 335355 316446 596849 429926 670037 936762 167984 894126 535944 888009 752748 305866 705266 053124 565726 661068 233608 269457 851908 671080 046819 285119 962346 622774 291000 862621 159855 971637 503135 183902 617690 971515 897735 771018 622696 912522 634613 789706 318332 263992 550417 761729 722439 149424 391508 497095 931594 777651 169892 639468 788236 206215 048747 775895 010731 802315 539948 151959 695782 587555 459439 933674 991354 203746 422798 529103 441714 728370 308613 135308 748756 046725 052084 740350 448868 190094 216569 776055 044554 708938 036498 725925 079506 187861 / 82 > 31781 [i]
- extracting embedded OOA [i] would yield OOA(31781, 298, S3, 6, 1639), but
- m-reduction [i] would yield (142, 1781, 298)-net in base 3, but