Best Known (16, s)-Sequences in Base 49
(16, 65)-Sequence over F49 — Constructive and digital
Digital (16, 65)-sequence over F49, using
(16, 91)-Sequence over F49 — Digital
Digital (16, 91)-sequence over F49, using
- t-expansion [i] based on digital (3, 91)-sequence over F49, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 3 and N(F) ≥ 92, using
(16, 849)-Sequence in Base 49 — Upper bound on s
There is no (16, 850)-sequence in base 49, because
- net from sequence [i] would yield (16, m, 851)-net in base 49 for arbitrarily large m, but
- m-reduction [i] would yield (16, 849, 851)-net in base 49, but
- extracting embedded OOA [i] would yield OA(49849, 851, S49, 833), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1392 481002 861691 539575 861783 502855 857538 042672 189362 494442 511592 704832 138983 917895 921068 361820 418218 094569 347591 559661 587475 579819 005706 314909 156015 730856 315483 301531 399483 056426 896251 148894 807438 662050 287504 764734 043912 457474 633529 861213 696208 577429 009832 475757 869912 000273 736597 743136 067304 328277 993717 793412 195033 411999 352351 132634 785206 564148 987181 357702 100740 753307 871742 420021 777553 829681 744120 912917 445568 780410 338765 740428 811563 707720 026407 751510 442994 396910 153586 682012 406281 487915 812084 406976 021511 836331 961460 327694 217721 265788 361935 666662 686636 480033 702185 643974 115092 737935 563153 013523 895075 618834 299166 047783 267460 385405 597137 962972 832392 893848 405937 907566 418214 163720 679876 084466 540988 312420 680958 921726 507608 406408 901225 776416 524683 715574 541874 299985 676357 016680 976708 356072 359110 112173 433570 673150 848259 280528 857016 926123 055090 499177 054738 359132 152143 469566 799729 048193 952431 264541 193864 280983 303390 512480 972318 002503 621791 651364 746684 756835 217028 078757 127086 383156 952770 318576 296780 267178 661702 421127 566744 512016 019298 658919 592452 404179 683258 956781 134116 645636 994844 534302 873029 715695 520748 220197 714642 988034 917249 750335 500871 629269 976043 458769 840929 094702 309394 691196 286767 843461 317198 347771 391992 515430 403931 303417 978445 372396 888931 387117 633791 326878 409069 645217 965390 943130 428101 207202 529214 779358 465104 747260 662428 869075 456260 151619 841638 478209 968542 582645 932622 484149 313113 498125 983692 553888 626658 516149 832131 060003 / 139 > 49849 [i]
- extracting embedded OOA [i] would yield OA(49849, 851, S49, 833), but
- m-reduction [i] would yield (16, 849, 851)-net in base 49, but