Best Known (103, s)-Sequences in Base 5
(103, 85)-Sequence over F5 — Constructive and digital
Digital (103, 85)-sequence over F5, using
- base reduction for sequences [i] based on digital (9, 85)-sequence over F25, using
- s-reduction based on digital (9, 103)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 9 and N(F) ≥ 104, using
- s-reduction based on digital (9, 103)-sequence over F25, using
(103, 169)-Sequence over F5 — Digital
Digital (103, 169)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 103 and N(F) ≥ 170, using
(103, 429)-Sequence in Base 5 — Upper bound on s
There is no (103, 430)-sequence in base 5, because
- net from sequence [i] would yield (103, m, 431)-net in base 5 for arbitrarily large m, but
- m-reduction [i] would yield (103, 1719, 431)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(51719, 431, S5, 4, 1616), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 61082 198479 674607 233677 284403 215727 693114 165976 646970 655028 273471 143731 926584 925067 806672 494355 150950 993979 623361 253254 274784 181327 405271 945153 683690 604551 541146 718416 907768 446043 194198 144062 703911 833828 822063 595345 845453 838255 429820 694407 717159 143677 669236 231411 172041 825218 581587 706261 551777 513682 167538 084898 534515 008294 040326 417663 131019 778894 366802 595027 734270 542407 544525 456101 293258 287058 715816 719898 158840 955009 160442 400593 088886 471347 743143 040756 541597 989036 071300 945603 637904 549226 103316 205743 164358 972563 214523 306115 831069 759681 346157 153335 357921 901298 703680 876275 879769 433337 540506 578106 495360 381188 997594 283362 046276 344887 149555 377402 828820 911798 780201 693645 022288 935892 799495 631070 576824 573028 596075 813959 741318 119746 975639 968921 701927 424780 241942 654950 400376 436020 994234 177746 535463 179766 104331 015352 020864 183865 686214 407709 571827 790014 529549 407047 912749 393689 608466 846878 900247 096727 667908 200520 882239 008316 385833 153673 697360 608806 334510 864875 346458 072775 682435 228503 261794 211681 533050 648481 083650 979667 447862 600687 218380 689301 075137 037327 981434 297062 805843 819738 892131 338688 759076 136638 891602 197395 212240 049423 979752 318783 423219 382606 575225 477135 195062 405870 203292 579390 108585 357666 015625 / 1617 > 51719 [i]
- extracting embedded OOA [i] would yield OOA(51719, 431, S5, 4, 1616), but
- m-reduction [i] would yield (103, 1719, 431)-net in base 5, but