Best Known (125, s)-Sequences in Base 16
(125, 255)-Sequence over F16 — Constructive and digital
Digital (125, 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
(125, 257)-Sequence in Base 16 — Constructive
(125, 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
(125, 532)-Sequence over F16 — Digital
Digital (125, 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
(125, 1920)-Sequence in Base 16 — Upper bound on s
There is no (125, 1921)-sequence in base 16, because
- net from sequence [i] would yield (125, m, 1922)-net in base 16 for arbitrarily large m, but
- m-reduction [i] would yield (125, 5762, 1922)-net in base 16, but
- extracting embedded OOA [i] would yield OOA(165762, 1922, S16, 3, 5637), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 460899 601051 870880 752981 328523 861225 885402 917555 694968 378278 205861 705284 441092 594478 656838 898662 120625 164938 464477 639850 423543 509371 156835 996269 604695 356501 037491 617394 582232 395137 831964 829510 549186 240100 497217 467638 499788 502127 074700 172805 139394 752284 069057 334528 155476 485835 229724 102270 731519 289572 197696 855978 539388 642620 073424 385564 537908 353856 983703 766865 620503 787378 533860 807467 578714 783436 143245 292997 648008 334603 781975 645318 964367 658963 819243 748047 041073 273386 698757 543278 059174 877860 189118 957711 720724 315451 468730 774279 630835 976347 579659 250947 613637 978331 108949 655381 862591 175929 106613 913157 669316 021715 185137 370384 368101 005765 128895 794573 230343 337711 640081 006309 715132 594262 933586 111552 558165 679270 419877 639674 310273 093445 419373 077519 097432 222093 744206 902479 636717 208573 920884 357895 636835 832573 569912 823141 209079 593831 759195 308549 595452 984127 743595 273351 812260 558965 068489 527332 086140 550038 895264 466034 462346 711966 775499 145719 209620 358818 948027 022180 321923 392649 830235 101075 486117 317219 461006 112713 151501 991192 426620 875172 360586 547204 614032 928542 094564 166629 835987 033171 714370 181480 877767 636666 895447 160669 119925 935594 787331 262465 223216 041081 251915 747675 053484 450539 037092 898890 549172 534000 204926 429288 550821 818717 010746 911223 855758 126556 390563 534675 794207 634863 815440 369488 291313 271364 619105 519400 092952 726145 864221 387809 184609 211853 883238 470314 433806 805461 650026 128252 843163 720930 912959 897447 758460 842648 114131 955640 677879 156687 784337 071280 056018 131743 487358 572761 726045 926445 853183 329612 288983 601123 308085 594871 269814 205411 459717 729812 625991 209775 965050 655123 814823 997790 527630 923322 685809 508671 782011 035246 303425 589825 153945 344086 950433 626212 694176 370008 327139 113240 038430 765456 777647 681556 662773 137159 216728 673824 427444 330472 625555 177431 151483 050086 053410 325762 635951 530714 318158 451686 982667 609546 472090 413276 186373 201338 674103 614942 818075 555976 172090 974161 711753 794575 434407 372408 237223 123002 487849 013931 024651 803427 075782 504512 337265 984885 710191 647312 668576 645298 007865 648239 269557 465658 204985 366117 162357 884863 062295 654479 927760 257811 635786 653444 126886 059849 678753 394892 852104 350099 911312 750771 176642 674480 038421 560586 918424 517372 599430 360808 560352 115938 272637 199138 461630 974722 826257 195193 649026 266317 541613 326285 549807 837884 110134 253875 655379 733485 131703 189979 340797 928652 481059 547072 149720 432556 839712 244899 244367 858762 266158 224601 829138 984840 072991 699552 340486 616224 705773 782645 058407 536302 668968 569483 439385 406666 237259 244893 998864 061543 883179 132593 121896 185538 133650 566733 486209 981252 789011 255791 117502 483933 619021 751400 300700 313167 401777 135972 137459 414022 610910 431442 835898 836554 862884 290747 340661 054097 629802 046708 067435 465285 399925 486316 549995 390154 683972 014476 225680 040082 637748 777274 505335 840696 809472 266593 177526 273747 477164 266838 355128 036762 469288 439198 357245 580942 622985 175754 147706 726833 848156 462690 061556 417023 798563 300345 180864 024169 747130 513154 491720 258285 130385 359849 439448 308561 040885 661537 628345 283118 775470 494122 378717 847342 415839 038988 488863 304393 907553 061748 803886 680901 007760 661205 909082 663268 420936 633133 380100 453518 907759 999389 939223 700154 474438 681118 780309 045879 686716 627642 193442 340845 656436 212900 169832 415947 787594 919401 129558 586767 608038 083039 086621 647056 680021 650091 471996 273115 629352 604146 293951 572176 497007 048217 497706 992746 658922 114724 128404 099865 676908 876802 536117 362991 353483 156696 965419 513329 671814 053416 260709 185150 688677 588842 196981 905624 200577 377598 868826 762805 233270 785037 692105 504101 270656 250836 487322 890679 212016 061752 200442 158258 993450 014094 427761 002729 162223 830310 456928 465305 914702 484644 150023 430963 998081 889355 585767 317545 692197 010455 211252 071082 404694 356731 251312 696557 713630 801175 243520 703795 730760 510252 651411 088817 337118 897906 605058 798428 247757 302906 550753 315385 513513 360336 983647 160336 251696 179602 836163 989187 752039 542510 483021 771028 086746 080750 974481 765970 672592 662618 053939 147236 011879 768543 468127 264568 360143 893403 419332 352546 272236 501678 910925 293898 948326 118074 399864 343998 007029 388069 668703 899498 115924 793447 352421 342864 276548 137319 326877 365588 397442 196231 056868 621561 920625 521332 687343 876710 772518 509633 642309 485593 799001 913490 794557 691678 092470 783573 735976 455123 695226 112903 585914 907973 112840 953203 546543 850306 657481 261382 348386 981184 980746 432102 611370 821978 924152 105900 337234 065827 819671 831373 299427 561872 440384 235666 703714 547638 386752 350633 944246 518194 383001 498451 232291 361670 655251 874834 108328 454709 139000 968608 950430 227380 028858 806107 618761 173681 651853 433266 864832 656147 076911 521180 851752 325108 932410 321842 690361 463511 050791 248810 673573 493642 020931 662144 943960 083033 540969 533009 458762 921500 804744 887675 910335 888051 025744 745026 057143 846000 415124 469111 948986 130499 034136 861346 633054 660440 125611 705328 307450 973653 434765 348690 156492 989871 673931 999815 660403 742023 943957 128386 355708 337331 373646 913607 077064 870891 548018 595864 022454 410037 140513 111137 650071 197238 454792 369457 045401 373220 252777 362925 036271 288347 032974 371588 628409 722453 903413 602669 078652 929084 310032 840547 806890 087602 428610 783566 961714 189943 757489 510388 752491 053814 639154 421082 651179 480949 258248 311598 246412 981498 188918 074051 700773 691694 437147 540180 663334 434303 484625 699007 720155 274163 427917 744053 971694 669047 141010 844757 874482 286954 339935 701213 971361 408243 737946 884847 397115 946547 771729 554697 799597 739179 171051 366569 101005 417102 942719 460951 525080 413357 392012 561435 718153 601131 782076 287926 733210 847884 414149 513748 538521 948624 845706 269200 683709 317658 574720 577809 743207 935948 061983 679451 532909 551233 772957 156863 181961 870822 316839 163534 383851 564100 519066 357241 555266 141428 424862 172943 282736 742741 794529 516116 472117 129469 825210 231621 884916 829663 860421 014248 173864 748604 355044 319388 019488 023811 323045 731451 141103 195785 795930 600980 195635 592972 144147 767692 807493 967101 860269 789289 522317 620705 224582 705180 693745 747788 349537 749183 137106 898111 744055 528191 811043 752385 375099 538079 327093 836103 579039 747573 473311 360996 460992 503286 129406 720378 270170 543815 957835 656268 220864 257591 716658 394099 306821 777442 167674 791412 087753 265437 422597 739286 294794 646860 337338 864302 688138 713846 820201 232355 606821 570978 069228 559998 791296 952072 827441 830467 844586 652340 928429 228490 696828 325201 876212 631634 489674 695674 481835 042745 368579 033505 049699 192788 285518 565986 311367 294431 660174 238324 382895 225451 751018 947879 247819 142042 465525 024115 117869 804173 329407 248945 465500 725750 673265 893792 313220 667845 449815 030219 464091 654094 853801 503417 365121 308706 544565 191411 647926 117453 154086 274283 557277 683698 569831 600772 433900 216242 964849 147734 892153 822456 734223 098437 297435 131041 995509 092643 734215 266226 804227 381989 050213 967621 798507 957332 548208 276834 908100 809800 364479 193310 873636 276943 472868 820226 777277 037269 834948 243323 814129 416623 414313 838285 505524 067451 940408 223278 132236 305060 799671 868413 411125 867996 329145 276079 563543 480528 416385 706711 099337 207757 958780 697314 584790 767254 139611 625647 096987 831946 044815 413584 630525 321751 762225 023760 666650 625601 680616 226682 182763 370471 515557 793337 089679 958003 415661 487663 480929 412627 930490 020080 929635 339981 553664 / 2819 > 165762 [i]
- extracting embedded OOA [i] would yield OOA(165762, 1922, S16, 3, 5637), but
- m-reduction [i] would yield (125, 5762, 1922)-net in base 16, but