Best Known (6, s)-Sequences in Base 81
(6, 159)-Sequence over F81 — Constructive and digital
Digital (6, 159)-sequence over F81, using
- t-expansion [i] based on digital (5, 159)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 5 and N(F) ≥ 160, using
(6, 189)-Sequence over F81 — Digital
Digital (6, 189)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 6 and N(F) ≥ 190, using
(6, 573)-Sequence in Base 81 — Upper bound on s
There is no (6, 574)-sequence in base 81, because
- net from sequence [i] would yield (6, m, 575)-net in base 81 for arbitrarily large m, but
- m-reduction [i] would yield (6, 573, 575)-net in base 81, but
- extracting embedded OOA [i] would yield OA(81573, 575, S81, 567), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 2953 934331 509876 725042 481303 291341 416260 356383 503818 510234 696915 870270 827186 567984 807735 078379 559447 719309 624916 517791 700236 339256 399406 300158 816433 916515 306807 846485 800733 180609 735743 717271 480863 858512 017295 762218 351973 798783 517258 006537 244692 394677 404646 923592 887532 842945 425895 546572 499533 582733 867392 352138 746907 918209 389360 006655 459868 790409 254860 501990 117410 111654 751087 587195 582088 947337 674315 473661 233984 885652 279097 933672 127768 911057 955464 794485 982862 984188 087771 975561 147715 967130 188272 152738 811758 450186 196441 518564 797437 331282 153233 752568 532798 798711 029566 770148 495256 403449 951114 536528 268447 995112 699681 166959 036534 183801 039343 763624 633437 485340 669989 312602 155847 701377 001908 883756 863378 730458 343440 878783 147732 009441 042183 686461 674674 005726 697116 390109 386378 142039 841634 318384 825158 030585 223047 585893 371143 910994 191050 056091 094377 782146 264798 422856 615419 307352 431273 251247 309033 278796 249793 799950 716618 211191 083115 853726 029361 331561 547330 836612 278357 898193 563350 069764 591246 810902 879894 706934 183751 478746 557452 684493 591320 660534 507585 796956 786863 014790 420014 331432 188006 071838 580321 / 71 > 81573 [i]
- extracting embedded OOA [i] would yield OA(81573, 575, S81, 567), but
- m-reduction [i] would yield (6, 573, 575)-net in base 81, but