Best Known (128, s)-Sequences in Base 16
(128, 255)-Sequence over F16 — Constructive and digital
Digital (128, 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
(128, 257)-Sequence in Base 16 — Constructive
(128, 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
(128, 532)-Sequence over F16 — Digital
Digital (128, 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
(128, 1965)-Sequence in Base 16 — Upper bound on s
There is no (128, 1966)-sequence in base 16, because
- net from sequence [i] would yield (128, m, 1967)-net in base 16 for arbitrarily large m, but
- m-reduction [i] would yield (128, 5897, 1967)-net in base 16, but
- extracting embedded OOA [i] would yield OOA(165897, 1967, S16, 3, 5769), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 329386 504430 531250 368817 621014 009661 309981 934147 584781 373687 480687 329772 623644 991644 187387 178512 182867 358644 602231 300781 935713 766411 431762 898714 947238 237446 002188 103838 710145 501640 379324 809574 353250 647486 876888 363102 286735 923190 524175 828674 386247 471384 659264 221168 693537 931554 910029 458222 273924 276781 323969 599036 969096 265149 801844 720907 334154 499505 565496 327932 986548 460699 526852 672225 655080 364193 069724 275627 381616 984080 870034 832021 945212 746694 569412 527609 230209 629809 327018 562536 017874 341227 880544 914860 447657 870788 570847 993168 173604 711023 381074 773092 680009 029257 177941 522946 304106 960063 513287 143980 806083 577065 198557 623709 392680 206965 850407 812745 453875 542903 700962 463233 642130 814220 548361 954745 806945 489009 505270 366163 628087 643609 818886 847235 300638 794581 591151 308564 950003 590706 947970 204991 556415 040063 802914 190124 516050 802788 659440 914262 825497 424944 795038 530221 104783 311902 941560 367043 632832 118544 338868 483021 154293 837020 948451 442123 489775 292879 809187 612322 215188 113842 762580 939864 852538 809105 665466 905856 791905 939159 937961 025738 500365 676672 687862 878845 731491 821768 886429 183071 468076 339533 277724 548067 601025 595022 026926 924935 539988 420544 645525 582938 710019 144158 916400 329489 890728 918389 264804 495495 921392 312253 051757 708026 975798 652567 506002 540146 732439 172108 340718 611259 575207 499301 658110 043943 576505 583872 235867 989684 291526 410517 020779 553594 572133 088342 921632 294160 149968 918292 474650 094690 011186 886516 901922 203291 947807 727541 297048 270161 701835 244770 891364 333769 848645 968755 867003 555660 431047 158751 594963 754824 996683 720238 635037 395193 461000 122484 911312 529217 920116 290213 989991 934266 661372 588951 179851 937540 776236 350615 029663 753434 325202 735662 521238 564958 271562 992572 972235 145235 312472 651941 646590 027239 354605 209137 480868 822763 936540 425494 988618 389409 433712 451334 403108 542269 689095 965416 176937 420679 868394 854397 052369 747863 442244 592035 447617 322228 639171 114649 232666 388173 069345 324416 574699 329228 434543 254667 919847 168199 961110 338533 198342 767041 061912 851663 321818 073206 478823 267267 091914 002919 233929 654338 408017 984408 240249 510676 156454 565958 330486 891148 088086 947634 108069 561286 305373 173906 910219 799754 711744 971130 606229 732147 123362 332820 677456 348382 115189 757188 486974 729585 135498 576896 659512 139393 668737 336225 929326 166503 061184 999318 167305 594916 591142 687349 337076 609993 608318 152396 812603 691320 819400 177318 323993 463408 822311 544384 949458 573585 396282 484625 861082 072752 152526 615436 100644 581208 671410 195494 036003 357438 870479 741514 072713 685801 823819 877963 173859 311875 105912 337756 172455 780968 185467 383672 623194 002214 141318 867969 249873 026426 416760 432535 333969 282729 375878 838647 871166 325300 855899 456676 603688 573304 817116 776275 818861 103713 695429 727431 503662 049013 667949 426665 784380 583516 409470 403684 440155 964082 831667 040003 520297 634670 427321 160043 431881 352782 256833 490453 691569 818447 262977 425089 966085 366072 326773 626055 398227 207373 471756 113691 996477 831621 550584 496724 944434 090693 714055 232234 283212 946707 625765 604697 552386 789354 422957 957864 143774 183401 246293 404837 178920 344210 194577 713834 398783 274396 454331 182235 377134 243717 742395 617348 090898 917829 497487 313774 955401 164996 905455 785680 080966 835460 378404 216471 779773 358665 392071 944683 726900 758627 851552 621563 657964 336771 369527 135003 809982 059352 858121 869102 876496 595588 831691 800118 209073 092796 012897 083950 924315 023601 641296 314169 877494 965201 003397 711561 861684 153589 680472 216670 479172 705306 938822 287019 518967 623779 087406 520952 919573 510969 290023 473288 814104 627202 732713 509897 540646 664126 136726 101682 759918 200299 333309 508475 098167 703349 866700 489879 559668 374701 033841 206253 289700 154542 739336 292449 660287 339512 304555 301602 851622 149140 259786 511340 410133 640832 119949 479951 264630 783349 446898 104380 368790 442369 037497 744250 946518 554336 872019 376981 702839 961945 153956 654129 410420 543085 569364 666833 891921 014563 811111 133505 869779 867919 832883 190383 379170 404590 043880 898977 292543 370080 492323 638259 773938 873956 149544 105657 467250 802743 084478 270914 259358 725730 343983 856130 652358 194082 798638 088981 381746 275652 778714 685910 102114 679204 377182 570190 576548 181716 438813 158556 569296 830146 318439 426759 592517 010768 819722 065414 351422 695731 293995 100221 193050 008131 941322 517922 901874 599879 503254 131732 176869 840093 542762 829362 677531 641097 087364 745707 848480 271052 050517 866250 931366 661184 109064 137111 330395 370877 505359 744912 727515 177460 233049 104984 953117 517112 140382 598478 361180 705573 183976 889189 861889 708091 094139 946459 138303 815426 505900 580175 480179 064957 031094 923981 058951 325617 627648 536160 707897 781894 449913 405404 409855 822932 728905 401119 168534 098377 117165 885519 135152 427386 044789 965270 195881 120273 212585 833136 107234 631422 501886 225688 967618 707335 477127 447204 342145 860171 850811 140938 688594 761535 425779 391688 126928 482518 637403 905019 638281 257536 766981 316281 785017 323915 037800 099585 277490 379220 540293 943108 367225 156666 160226 448520 172396 862359 629247 434316 167604 117099 847069 151132 205180 384798 101013 655657 211685 853142 235063 373819 646578 704299 087977 073220 542956 587770 989268 024681 052689 194422 723574 515666 759415 569990 447449 784066 079829 456038 338084 114756 248597 677976 101829 415465 273907 081326 037356 469090 137441 746202 821800 867469 541859 952546 216837 108504 666735 680341 414582 181349 051339 604991 862681 006265 185981 739394 284756 493853 978504 668334 142044 313894 921783 306453 973401 205394 271931 732139 039126 802893 211917 450610 485605 759861 191415 965021 398279 776254 104445 513694 677477 779462 549037 320887 692828 758529 067885 366596 794364 216094 093880 544763 630978 158648 594272 856985 088078 890709 305187 211498 434823 127760 861239 645942 024831 802608 823211 127760 034778 975534 924213 568436 656356 994932 526507 502092 018538 085838 294642 656045 306554 508497 599363 979802 530961 613635 135296 963432 238220 939257 093728 978628 901269 922430 328146 861647 064188 201667 604859 255227 390777 150819 566875 288455 193636 417439 487612 881877 820762 309825 956159 705162 205137 851683 701964 914593 219792 248272 741944 169766 617288 885009 859518 224148 079546 335841 591146 800497 809524 336263 043031 405533 757898 521143 691833 109545 812497 138220 426136 407747 217955 067011 267906 264646 011415 068281 945342 207218 666204 055986 131138 558555 635601 079859 213781 997262 598714 244310 908270 870326 518772 709429 888380 838817 365167 948480 716859 963152 060782 612373 181394 148757 330217 198339 713841 922457 448865 158751 004568 131806 246545 679958 067394 922388 180387 715371 040527 028929 654690 900520 467789 609412 125075 214837 509086 188736 331829 087190 772061 712757 881478 980561 872777 472598 201802 248479 095905 726144 349719 323582 646222 467813 429813 567559 133931 384676 960710 259905 462162 154402 515585 594610 932097 271101 760618 213346 585713 996011 729004 585667 231224 644407 430638 534422 100243 758502 774732 586252 339783 083575 303973 055509 023244 258758 819126 301943 954867 319882 731460 569985 591305 450454 277638 545545 669723 091670 246003 888705 597467 696586 260274 286243 243813 112500 781596 310348 028870 764080 261556 734213 601243 631101 153801 564225 808099 478278 741987 935303 201746 008656 847037 778784 037512 383738 545432 874341 314945 309783 017176 277085 045259 845038 262336 188821 079314 651355 879508 310022 168823 852233 179658 702891 293816 913789 486314 076962 677499 978069 581387 142993 615266 550571 789137 390099 917290 232389 689998 023992 605168 715000 648061 112119 379215 444913 357554 813126 546969 754457 524955 598675 718037 017044 697580 962773 045357 433596 820763 824251 778112 205138 767358 742447 478548 980485 531780 197722 524159 496567 556285 661184 / 577 > 165897 [i]
- extracting embedded OOA [i] would yield OOA(165897, 1967, S16, 3, 5769), but
- m-reduction [i] would yield (128, 5897, 1967)-net in base 16, but