Best Known (130, s)-Sequences in Base 16
(130, 255)-Sequence over F16 — Constructive and digital
Digital (130, 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
(130, 257)-Sequence in Base 16 — Constructive
(130, 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
(130, 532)-Sequence over F16 — Digital
Digital (130, 532)-sequence over F16, using
- t-expansion [i] based on 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
(130, 1995)-Sequence in Base 16 — Upper bound on s
There is no (130, 1996)-sequence in base 16, because
- net from sequence [i] would yield (130, m, 1997)-net in base 16 for arbitrarily large m, but
- m-reduction [i] would yield (130, 5987, 1997)-net in base 16, but
- extracting embedded OOA [i] would yield OOA(165987, 1997, S16, 3, 5857), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 3 849250 719909 029259 566113 277649 509072 942729 142849 246210 780354 202847 995652 469557 418395 554899 344475 985496 192152 104439 299191 945764 715865 747203 674139 486703 757483 179162 686598 362230 446658 467075 656789 530675 319652 547509 580286 131524 361836 252637 405749 167333 357374 519715 662671 622677 375090 230704 659043 752376 127035 475630 244981 824756 291173 978527 759482 043639 560435 196181 137268 136255 916308 594025 196388 525883 234593 618031 195439 702547 343459 807596 002260 302506 351981 457305 915974 734877 470375 218906 456275 424062 954361 530628 696190 641202 933258 122499 747837 095650 967896 011458 687950 963734 069513 320031 432198 805846 708983 884810 279173 626771 474917 291945 140983 455972 288274 933266 925417 412998 893614 709816 063259 424599 856838 205332 689656 451069 986310 821137 398277 942629 434426 238337 991028 807868 096836 450903 020546 814401 170146 590360 767062 456522 796569 528066 113743 390259 639439 733378 268205 333042 547521 600136 260357 356227 542271 320426 780062 474620 866877 397988 427385 824044 635670 634374 838163 844304 653661 615415 925534 592953 312146 389444 481365 451661 967985 964990 245936 939102 141320 794237 783689 884821 740381 477252 654619 450425 886346 970869 400736 683822 567183 017274 887972 562014 092985 999007 545999 291960 300290 957243 551642 948282 522930 694732 734088 716895 421528 791485 246976 660110 663485 070892 268253 800019 709357 351937 656146 676740 430126 920491 620507 184359 137367 397316 983064 769720 189875 852907 646947 033143 899583 548248 570603 383925 977457 429053 238371 545384 387070 193956 172910 864171 946821 826350 058063 999115 007699 252144 757038 392154 533772 202822 770721 679968 113731 039522 707494 970416 195736 441436 703746 124381 854112 761044 778914 663979 789327 017892 240870 893040 139134 873994 837668 078811 478287 363779 225892 280217 312675 057958 535851 093165 839600 645715 051054 760986 038980 321989 446785 751065 380097 682522 526719 458559 388840 426696 322456 162615 645532 538459 443865 133873 635463 910713 403538 299791 215914 261857 315179 470305 024139 032080 183903 170836 664100 018413 047622 033923 586531 718978 680253 245277 645276 082542 599123 006560 311801 752623 906057 080695 391654 020594 136228 201663 238451 902581 463575 045516 643994 582301 451302 009350 604375 669486 585930 131808 103997 492525 451392 869078 901120 274616 678157 468898 018293 551608 287737 428348 574093 448273 934467 760936 585205 390307 841245 745144 672708 649309 188891 715031 430490 766675 007838 798889 450996 818491 745196 671298 728860 308536 645538 654867 992011 564293 288768 012339 732329 712800 467754 185591 465370 331108 473187 109130 681471 946724 622430 244470 622650 566092 412121 977200 361042 214963 709550 028351 105187 593954 032025 766817 894912 253413 875005 945494 273717 019712 782236 821830 819984 835819 534334 073745 434039 120707 817146 719617 824630 559809 596853 803490 598786 502964 293987 411593 632271 121316 337506 430853 590927 317295 833317 666318 739674 286012 036352 064489 338680 998062 143092 603645 194425 190803 335394 398155 073475 141196 423885 879568 820024 419818 097934 964172 326517 718231 532453 250921 646168 875010 629844 818844 766013 311354 848559 356544 061319 316326 088291 273907 968405 590749 443294 606777 889266 069278 859117 418908 012437 033098 302374 138002 009920 107439 401668 990919 410223 024499 244525 268458 393275 542106 190171 428022 598950 118199 132330 497250 323164 806042 340924 173899 335749 128894 505430 800167 468832 547992 146369 517308 828460 139385 951957 499477 868898 568850 498165 233420 484575 594199 343751 424547 144338 503819 221644 745117 957579 546426 937079 050208 500058 794713 262710 603233 451818 187061 794619 004963 810332 430695 744592 266820 419016 628972 453620 802099 202990 688981 751392 310205 744807 002725 876582 422263 374226 256923 898803 413095 601418 139705 092189 780167 576765 652216 163945 812536 242688 272089 587326 736459 302924 386862 387411 054057 993518 747626 964001 425811 517490 132021 978904 395375 097650 570827 137274 394459 546502 789674 514642 526519 127266 798321 039516 865515 300561 141270 366687 768985 035777 273853 454779 248992 800369 504853 149172 371776 280389 837902 875320 499444 559564 988896 826424 309472 480116 830283 559958 153299 914160 370352 501026 916533 208728 846868 215203 951401 393594 071665 899027 498002 066327 273807 653696 832437 463761 615290 812096 505527 389948 060072 845778 597759 724838 583208 513541 933690 037732 214095 641101 080592 994511 728637 592281 870193 342067 008485 706142 276629 547389 200622 431758 525610 472484 721614 023088 403925 685139 294528 169981 449905 675999 401891 758884 002321 251262 691902 419001 557348 166296 758825 609959 630006 821556 591253 299734 170281 297291 774838 003709 039933 194620 933121 101024 869024 767212 598969 681391 011511 726916 944187 691183 007448 119003 561521 904978 393210 420002 694070 481693 824621 497050 655634 311099 968338 949444 202577 677599 570434 683127 371107 086070 262657 490329 624796 490708 108584 232164 590022 782996 531153 908200 058895 617367 536743 174628 634774 157233 745797 543765 671022 115646 404734 424255 655629 086187 960321 998831 485834 584431 949815 296207 406454 469817 159478 611486 941055 558093 271332 564521 746431 147838 031977 465853 874348 902846 188105 997899 057846 130011 957675 276474 599183 902237 131839 251081 166703 842800 537447 746184 921441 219455 236067 890107 658381 228901 338615 680287 914004 607782 598086 889734 450422 914463 239858 311894 728021 596936 776100 406873 986704 097561 286678 474904 060576 779855 843938 371167 135672 342907 928738 391289 906424 982968 916324 856971 783765 392139 176877 373889 955039 221464 342718 913421 895105 711443 807267 508220 198691 108642 564617 464718 234780 224380 147910 968998 245215 972127 492643 080825 357311 996172 716875 015191 932911 150158 132972 115349 764373 613063 629744 468806 190352 886873 439477 450384 301417 323819 147694 728141 266968 340885 327446 495031 639761 644499 521230 070933 214480 636065 937706 890139 338680 345332 132702 624210 816370 502793 202818 100167 851433 222132 928882 686651 728666 217378 529041 723743 393776 653019 710584 755409 418998 836532 767193 382186 449385 996844 021697 918101 586523 037978 382860 647140 759306 929187 157618 880377 932138 735115 487037 875100 749100 353841 110718 453374 280520 309147 035119 473076 252236 316285 744326 058145 629383 243266 299945 523228 346856 163024 062291 619881 208711 563920 898649 124114 620788 485343 580178 017967 322139 832460 944381 674768 895018 979866 923590 654889 787137 551157 999649 308336 436430 574017 917085 957554 550921 285870 519899 379941 672656 307178 288349 989174 547584 223064 802414 384386 514802 933969 020500 604826 025374 323624 832561 742228 374214 081768 679079 839253 192304 065491 164387 736930 027358 332486 091554 963686 492719 015033 011357 651233 141685 916905 363968 918728 625208 034341 637500 156572 184351 334424 765221 655710 637286 778640 519923 444609 545100 533083 406853 163119 333034 406677 476581 236951 335256 735697 505232 307006 387796 624474 997935 373011 166745 277258 260816 479951 545695 199184 000829 196015 786014 055391 570275 684621 099902 105502 323973 711751 584851 620272 422125 896689 269224 855828 988784 861031 613200 804119 301861 769576 111201 747009 047240 553128 888852 467095 799304 951211 236878 692075 128362 493803 242730 075881 418336 985240 160691 103200 809657 060178 502138 800489 639926 360280 657677 325348 640186 859784 240243 053464 917424 014856 960413 441998 843510 647644 431967 711511 467247 605265 067160 978099 673992 271018 507437 592266 880191 846783 796885 448831 329770 259651 145553 028546 741673 961909 912388 723694 271968 241423 965009 281222 794068 302619 855636 041988 419970 531302 021834 017256 921917 248752 542933 131015 564127 615801 250922 048161 930087 318512 738559 106856 313795 444313 974554 011900 195765 477748 271364 734579 169702 064171 352896 424176 133857 185557 220474 385510 568252 950271 332146 875360 819765 987591 316614 057767 011013 578554 789649 375394 676269 530251 368659 024496 533173 475699 721269 382574 994242 767670 556820 482215 704854 636099 928897 446067 784949 723684 352620 410792 588321 338814 428100 666890 810158 519675 930294 033048 842128 282838 449577 619354 637703 253175 094264 464484 664809 953336 228513 570380 109708 263424 / 2929 > 165987 [i]
- extracting embedded OOA [i] would yield OOA(165987, 1997, S16, 3, 5857), but
- m-reduction [i] would yield (130, 5987, 1997)-net in base 16, but