Best Known (116, s)-Sequences in Base 16
(116, 255)-Sequence over F16 — Constructive and digital
Digital (116, 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
(116, 257)-Sequence in Base 16 — Constructive
(116, 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
(116, 339)-Sequence over F16 — Digital
Digital (116, 339)-sequence over F16, using
- t-expansion [i] based on digital (101, 339)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 101 and N(F) ≥ 340, using
(116, 1785)-Sequence in Base 16 — Upper bound on s
There is no (116, 1786)-sequence in base 16, because
- net from sequence [i] would yield (116, m, 1787)-net in base 16 for arbitrarily large m, but
- m-reduction [i] would yield (116, 5357, 1787)-net in base 16, but
- extracting embedded OOA [i] would yield OOA(165357, 1787, S16, 3, 5241), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 10098 687883 062256 072762 100313 178896 304809 219883 914225 469236 858888 598404 705936 755787 364295 607686 112345 364843 794785 964406 548540 534740 775319 280608 635307 379890 731871 775220 651354 991098 185334 999782 136080 944727 461147 278725 198059 171428 438157 130762 065022 111097 765616 849193 275651 002607 678794 883284 154954 158773 780109 391851 704029 268281 902988 380468 575489 117367 900104 061564 296315 385204 254348 442633 340274 003884 781704 832921 498949 596915 036716 773404 217209 713610 089077 167233 044312 388345 323779 028416 388732 525956 607433 820026 066984 256542 273247 069479 577282 483987 024697 090485 654171 268629 417722 201086 159678 355982 811176 931068 223543 438771 364519 020748 087960 876771 801832 336871 848501 952925 175815 679519 583825 773793 957224 795863 584768 101295 613010 416745 321063 353360 307995 628332 919608 746386 803699 649530 040219 694533 805034 396837 078234 531995 906116 815415 403021 338081 411256 453940 657414 984037 553289 826171 190782 852169 039511 080344 037302 665649 311459 303472 978099 330210 295410 986291 876068 732595 087729 549494 319517 330795 432313 404385 747230 432502 917591 252575 133664 217283 349233 672579 649914 284516 648719 786295 882091 867159 932860 104960 160267 215608 922406 553259 893647 131879 769754 766952 532966 240693 206342 490248 004107 775473 551594 999761 604098 674683 682868 518384 893673 484699 513633 138537 450665 687916 072508 127058 379004 415811 389167 016616 064821 766154 891175 638140 324693 222116 322117 926279 319894 048576 603132 733154 102083 661119 500007 204221 755679 401026 474016 211280 698924 023190 214582 051964 500944 418905 874654 746261 856295 586390 904251 128484 749891 740085 532127 736611 215916 725515 768134 138376 835472 032325 773832 096850 493397 972855 903602 325533 669598 082623 077326 794213 052090 155676 150571 944981 138281 237131 278286 478591 915325 479663 427107 976603 934897 884214 332733 043874 001260 416824 941755 729084 545101 081967 914594 600638 406811 820329 731857 369120 408326 918842 418550 362089 043710 722559 225327 389555 237024 981584 295197 180357 237021 376701 001706 769777 845126 510832 807468 106208 618156 018132 134151 822204 277842 972977 863895 317023 172232 819479 168519 731486 822386 314928 463409 174114 079436 490253 253602 367529 490359 315217 016072 565772 009028 065696 044334 514038 751887 733003 924451 157791 820833 451639 622053 426674 558750 194346 112537 394525 702421 354861 152176 347728 416759 290229 215518 943766 739981 466981 628889 196223 539454 444822 721713 541103 588080 370250 186923 892040 234731 049419 459997 890234 678937 698726 217528 574007 809367 167066 475395 180411 348804 168988 785236 298759 780250 365202 984298 184582 963518 291599 430514 949659 858361 817225 105719 449785 689678 650672 161662 100224 094631 320125 246580 804031 643932 158329 686590 017282 887731 015743 666360 074674 554276 720236 963893 390154 812873 229707 705525 625482 935465 080053 664805 807537 733461 119626 640721 591720 044528 272273 651876 628813 547841 700804 584186 978044 968762 085370 796552 957061 975144 624618 140188 499712 046028 328768 708624 627541 296058 176973 879837 511819 205783 454514 879853 739568 801897 822554 559229 435374 197815 545230 100665 611041 877437 646287 027352 011895 317744 953011 347297 293122 715755 118049 405268 245530 986195 186511 414431 873325 407324 120600 751593 965162 040028 072562 147654 113373 893829 202343 978541 639813 450482 857309 977401 045122 056876 439552 670012 516546 697691 324146 646981 898505 781190 726224 223734 384145 143320 100792 724167 342604 902759 431087 181270 626500 205222 730023 993100 388380 559590 614302 724357 670221 934711 124660 601998 839891 950929 221787 146537 809817 814440 576722 398112 077129 539578 382791 625164 952037 901782 397372 776428 842055 170686 816337 284839 090925 613826 117431 117015 106776 238088 072360 133482 550626 298693 307059 093308 561694 876519 225263 314004 282463 831538 274542 254576 807565 451473 892353 386475 235840 601881 047685 326162 017720 395270 634736 120484 714951 007174 524843 150456 024647 761949 178154 813931 696547 756391 754061 015147 484005 819002 253185 765481 921369 913347 321638 161956 895523 423400 127697 307754 725525 862087 415824 071963 309063 000809 333171 201209 122880 435373 571591 977819 314796 060311 570233 947309 400051 149006 422404 962745 325400 274995 780579 336863 131152 835435 750894 930671 122470 612472 643717 948515 135654 454421 492476 044258 369746 017336 183329 120431 950593 747719 963225 820252 566675 254287 850768 853432 794685 080869 064652 533147 138403 986446 378020 683568 673552 778826 624683 093554 978550 697105 249814 932882 782772 681796 157044 669337 553940 149656 897843 123133 085795 172503 846686 594047 983719 503555 392789 187351 705722 571216 315470 313313 704604 059161 874526 357696 415200 636125 191600 781757 874409 610933 162369 497833 691083 088412 127122 489831 671630 356079 300188 101173 155776 560277 730885 131247 671091 499384 407578 454088 310869 296263 131341 466762 888058 166178 480608 681546 557354 277796 677616 852651 762094 503894 960869 116947 008768 824229 744632 905650 592465 802859 514995 710399 192529 071247 359190 231355 363589 642822 911279 964550 788183 856457 596514 545566 249556 511762 646451 289520 868248 252080 571774 660284 361486 735526 472750 361430 591042 076722 286064 296965 395303 343493 102301 001723 441235 575124 731429 510863 291033 184168 633422 129610 802813 451640 238147 692452 604603 500485 436013 360510 855410 760698 910705 815684 529739 363135 842256 822641 701282 098778 988561 948106 556500 681784 753538 436186 425141 832731 729691 861913 419060 839416 796845 948579 949226 607138 435559 891596 798059 468314 989813 343142 510606 843708 355390 285058 857268 792339 179684 609869 233226 558553 587385 919981 124859 473040 780360 630989 755239 811857 631288 808353 464168 552241 331105 304757 555998 561961 040303 829823 792037 112983 115519 258986 501663 182781 424457 324572 600388 560903 242596 863318 802421 716344 321906 894938 802363 237037 964896 290371 713400 384229 564006 168157 538029 722514 008249 472717 745558 145784 526997 006796 890577 945901 859196 520139 663388 218033 358715 791999 656059 228345 605312 480537 595406 626061 167608 280036 539526 414249 199556 533917 338600 906939 365539 208285 107069 189236 792578 086746 971436 935703 634800 919749 818915 536299 154781 480120 614824 144661 638341 198709 369584 839629 858345 631319 510960 315801 459966 836417 221642 770237 799474 600195 058470 030554 086025 422594 000311 793729 344331 946679 445724 061834 969856 561549 548838 180924 552696 601625 529339 515534 508093 615065 811078 265869 563549 944385 989585 150892 721941 134018 452703 684074 029631 663719 750690 098365 496974 381243 874837 154477 323365 003148 836857 234336 882244 231569 058498 507815 689865 653100 303913 762567 207558 375425 556266 155418 637453 822576 941584 047352 442731 523223 583930 742093 233431 898767 130960 227046 523293 144708 403195 418582 840865 932373 883756 440650 495944 785968 386156 565298 391248 173782 063885 354260 738492 176794 949970 197669 064339 552510 152826 835523 843418 817216 084156 818836 471437 306750 958869 418816 930041 463280 419263 914885 104806 939639 690468 706269 383196 323840 514324 256503 700695 203423 234877 791061 171097 834198 952744 917072 992285 118444 671718 928311 703816 964901 906980 158362 291384 451995 568740 208669 165557 217761 158147 854365 195750 365859 884185 559888 577038 069002 141696 / 2621 > 165357 [i]
- extracting embedded OOA [i] would yield OOA(165357, 1787, S16, 3, 5241), but
- m-reduction [i] would yield (116, 5357, 1787)-net in base 16, but