Best Known (123, s)-Sequences in Base 16
(123, 255)-Sequence over F16 — Constructive and digital
Digital (123, 255)-sequence over F16, using
- t-expansion [i] based on digital (75, 255)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 75 and N(F) ≥ 256, using
- F4 from the tower of function fields by Bezerra and GarcÃa over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 75 and N(F) ≥ 256, using
(123, 257)-Sequence in Base 16 — Constructive
(123, 257)-sequence in base 16, using
- t-expansion [i] based on (113, 257)-sequence in base 16, using
- base expansion [i] based on digital (226, 257)-sequence over F4, using
- t-expansion [i] based on digital (225, 257)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 225 and N(F) ≥ 258, using
- T8 from the second tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 225 and N(F) ≥ 258, using
- t-expansion [i] based on digital (225, 257)-sequence over F4, using
- base expansion [i] based on digital (226, 257)-sequence over F4, using
(123, 532)-Sequence over F16 — Digital
Digital (123, 532)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 123 and N(F) ≥ 533, using
(123, 1890)-Sequence in Base 16 — Upper bound on s
There is no (123, 1891)-sequence in base 16, because
- net from sequence [i] would yield (123, m, 1892)-net in base 16 for arbitrarily large m, but
- m-reduction [i] would yield (123, 5672, 1892)-net in base 16, but
- extracting embedded OOA [i] would yield OOA(165672, 1892, S16, 3, 5549), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 13145 879369 265562 119296 812718 625199 577362 770084 246160 529738 464695 950480 263766 882660 849249 683959 622178 056215 713801 215341 863648 005768 737364 792082 043030 630253 477841 013575 629528 200120 221268 584616 755272 133696 570798 516544 771176 028103 980542 900159 695390 654694 615652 743500 995651 208702 546517 436506 502547 998620 410832 612255 769859 580304 539099 854600 691330 113550 584647 995147 790548 964382 332672 462917 940686 382592 903792 936764 905756 025400 794109 612068 962199 972884 821436 578972 357851 897586 073890 059874 217708 641928 412528 238690 110272 636849 028949 699090 663355 942338 010840 621088 965237 179723 583678 747422 891381 230526 208505 838519 818216 341288 558364 907927 178061 468666 945352 811133 859621 415096 466608 647981 158702 012191 348782 612040 306685 939122 280892 293070 687889 601461 724454 411031 645492 736649 155418 473659 944350 196082 230549 230591 492147 629087 981848 081240 764908 598154 192905 871172 214947 845255 697194 009786 312487 911247 510756 981295 284378 961505 949800 652932 586160 583747 683919 162391 526937 032455 641058 287554 270512 216098 520268 415276 625439 130177 047253 001021 855707 688496 883530 661782 542261 695950 924463 704268 808808 687978 357850 699840 766921 309215 813336 227705 664941 703384 588917 945704 849777 858110 064682 518713 994392 072233 265902 994826 546000 024917 404803 424500 947666 953549 789662 676761 075549 816931 201622 076010 000738 521190 601912 977623 759030 243791 270342 213961 850222 654561 917125 828887 741102 342816 087855 904668 289293 442422 979557 959220 584351 832675 567053 021612 580299 779184 332327 027910 866957 467765 094431 955542 894409 505012 762090 553134 875352 541521 824850 628338 156450 147443 036715 671284 180774 532050 149758 048890 793774 966900 076879 698166 080852 898878 881092 507343 008249 398628 263588 482971 920330 583402 503032 988385 270229 708977 437153 552417 937833 155304 633443 154476 930914 950359 099248 941026 169041 051766 832283 592387 336765 657117 069915 478768 009069 782064 809354 655795 071534 674258 274366 422570 325694 998072 094345 012361 651524 439386 439986 128559 271719 560827 568361 341956 090002 121710 648164 348232 763987 540841 296594 408795 368196 906244 914072 783849 507763 574043 648846 812373 417570 858012 453331 323979 331898 237784 759385 096559 910199 431408 145005 026003 679717 791555 897257 904448 489164 831958 195783 916463 249513 316588 960363 785168 587314 058567 834201 958951 734710 623329 490996 749528 450904 810850 192787 732994 436717 649917 914216 810793 588133 164012 266029 877875 604088 938653 751366 415067 450400 393486 952624 804505 713058 262074 833884 670641 063223 854150 155094 168800 961243 340147 538181 263507 757659 837281 629619 674280 774965 357334 035006 576561 732770 935595 027297 375828 283582 231660 254474 312292 026067 750598 931995 600004 945020 190768 510916 821647 099695 203615 966636 093802 840728 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846503 637437 142141 129532 005511 224462 353097 731646 567352 161114 034149 894822 934369 649489 609854 699133 618203 946719 812490 337560 824865 636713 004557 017613 601243 876243 177031 409964 673642 460673 716793 203579 926503 084706 556002 484570 592185 208285 097056 617028 630540 902807 194524 099655 679990 344634 306879 617626 036955 842770 912149 389076 459494 861963 400644 406621 799678 326024 744166 189757 862683 593693 054220 484967 318112 353225 540589 801974 932175 446577 997312 920122 498617 993655 288995 336744 193913 613839 170414 227687 212938 741006 598527 932771 633471 004740 267603 839812 351047 400668 944512 954162 540829 837744 000691 063723 089677 808842 673147 128806 098139 836384 365127 784927 908850 077277 900938 023500 831000 646755 282598 538363 736704 487870 357441 754172 535585 120549 904607 515106 852689 616430 698410 449506 976955 217397 185699 220321 404545 727078 317310 839542 970706 161963 230077 008505 427132 925311 783506 743634 145395 842821 661234 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684696 386836 686400 868520 847870 897346 234395 442757 076611 549348 034257 396368 618861 151950 063800 181032 829138 458697 897795 988675 519868 040275 049516 881387 315789 023800 132377 606499 035918 788861 576228 606342 547773 726403 535488 244047 080096 796905 847293 523402 142328 754861 807286 777024 059695 443713 005389 556445 735639 457740 308290 768160 583639 853745 229031 519339 939492 557023 016432 227150 493303 082656 261651 162511 910896 076343 958223 469559 740580 245903 224202 152256 393948 854180 071637 816929 475445 542653 400758 755966 283847 518816 006746 546295 640272 238940 708458 984746 463878 866745 643664 301260 435369 024141 371120 967724 588245 858647 941401 394745 778586 545982 559102 582331 451206 360593 794316 523019 612668 323701 603075 422287 917127 634876 147927 894675 201405 579278 990984 505393 718283 317115 068356 344486 911775 132061 883720 828370 080512 046214 393933 031268 338385 310209 588641 033437 699041 655236 972242 549319 133755 427275 099015 657229 774707 406698 030993 123939 932171 216533 681175 453999 147649 635694 065421 919089 969678 510897 265600 277764 599093 512466 315441 564020 617811 066172 489246 452277 972226 215428 533647 217570 722682 956633 803252 159580 778602 532194 748989 880382 616468 401034 822965 390818 023014 401058 955643 890914 275294 095209 672131 203345 842588 930694 283920 787018 982138 487603 642224 053330 328109 835433 271775 625373 003367 074257 826531 582057 296354 302016 891485 944224 729224 968789 832087 307621 381891 553151 993066 212275 600806 124922 303696 829890 244926 595494 703714 716054 425060 047738 520832 799507 870428 423161 739762 337032 535740 471550 554161 838425 136187 270273 777057 755120 153321 355509 699012 537481 897124 259761 218570 761637 998887 894151 581761 844306 221958 896202 639148 266214 329949 123224 031504 071587 768127 018293 043492 109127 758949 865773 494658 187725 438267 988486 109199 202964 049589 413564 626939 767409 244983 474080 257916 744379 879321 775675 230141 615433 580544 / 185 > 165672 [i]
- extracting embedded OOA [i] would yield OOA(165672, 1892, S16, 3, 5549), but
- m-reduction [i] would yield (123, 5672, 1892)-net in base 16, but