Best Known (121, s)-Sequences in Base 16
(121, 255)-Sequence over F16 — Constructive and digital
Digital (121, 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
(121, 257)-Sequence in Base 16 — Constructive
(121, 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
(121, 512)-Sequence over F16 — Digital
Digital (121, 512)-sequence over F16, using
- t-expansion [i] based on digital (118, 512)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 118 and N(F) ≥ 513, using
(121, 1860)-Sequence in Base 16 — Upper bound on s
There is no (121, 1861)-sequence in base 16, because
- net from sequence [i] would yield (121, m, 1862)-net in base 16 for arbitrarily large m, but
- m-reduction [i] would yield (121, 5582, 1862)-net in base 16, but
- extracting embedded OOA [i] would yield OOA(165582, 1862, S16, 3, 5461), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 84361 758384 000409 285121 327595 132685 311607 302077 476543 376239 049992 083718 842608 403705 586914 250391 648220 900493 804821 716613 393132 097976 668243 680616 879020 691647 424512 531574 539300 445098 902944 226372 430643 837031 120931 605970 147690 116902 044614 807488 195384 003951 527102 138584 069889 899735 322254 916206 067409 783651 642491 818985 710142 959573 085624 397696 320014 845258 396279 643116 083644 105334 034330 867458 442062 420467 902439 794897 166490 473338 710352 324410 274329 374440 367950 396641 541586 265862 060705 853165 173654 963073 199843 909023 815690 755198 844155 188244 590847 657421 973109 354989 502657 992172 893286 339169 660947 204812 271540 111913 522792 993479 731982 301354 044812 293213 422443 228468 269271 891562 166995 513518 956753 681693 459105 080834 868110 062696 530915 500773 667373 935372 124308 955569 356059 340693 847218 755387 173318 253092 501710 819467 187932 217336 439777 903890 653345 551802 976143 028712 551066 449188 510826 497062 034691 286724 689284 330055 361160 521707 499624 212541 561098 266244 623111 712056 377186 009820 674088 519758 527353 814664 531866 918379 568148 158505 904000 104330 117365 619722 921238 918723 874811 354917 691148 277695 675590 698082 273518 729153 181292 584178 730413 229045 749421 279672 770546 620576 449371 091069 307919 471813 159227 399069 188484 476879 572753 236290 611582 203477 728908 021793 267219 324333 018930 646573 655174 648165 643218 233769 910458 342677 048211 640999 081581 396167 426164 888093 807542 914657 449687 933374 243542 477728 905690 246414 922176 763563 558004 594908 380060 589970 434044 474583 037059 465162 503512 338463 541267 771454 247937 483574 277326 933767 700812 048596 411409 218674 688101 994834 080846 711392 735471 622313 382299 674109 371775 140744 603246 274655 222308 991870 488180 516308 422281 351085 182989 252007 871597 133217 201803 885531 823130 818418 036701 011021 354695 138169 411660 216795 358350 442592 589926 636851 808287 290000 755621 943400 502601 074093 767090 042187 772988 531413 487701 462536 652208 358835 825782 946792 801803 522854 689210 499624 003838 282652 296905 002332 507013 186691 617038 533201 671759 291285 411601 089994 598047 180733 239366 216466 174350 695628 784318 650102 056610 604519 562638 772652 210086 037338 623004 782293 464463 602468 044366 931411 663678 428849 988059 169796 314259 273624 882960 156710 761275 654107 777869 892937 703093 734839 383228 293271 803624 547770 534878 485082 958141 828620 237025 621566 068582 713683 677884 440838 725221 542642 376451 007891 541156 887596 128102 843142 938302 011967 523861 040717 133187 548754 594702 727676 892883 144421 881677 881566 351624 942848 504830 542792 430618 544487 434854 452963 047116 125135 618243 487947 060834 474792 526107 220289 577127 532700 472015 123493 484222 244038 579515 058445 277773 068464 295927 119038 920924 819691 222231 810837 953989 475571 774934 144446 389033 824067 702716 464737 093170 784540 921892 679860 035176 967869 612470 220161 309939 151826 332776 965476 040864 940124 152840 948275 096857 694970 802229 288021 090527 676967 060183 896772 955849 820170 057983 934554 019143 635877 048767 794054 406609 247073 545723 852319 194964 548269 554312 446227 965846 015342 609655 431907 081896 806074 039808 924888 120880 504047 823637 307833 988811 681573 748498 111338 865944 764298 345981 899389 619240 623883 697208 151560 320260 999388 234870 530942 997334 295236 505854 464978 816186 062855 687220 422879 135727 443022 498404 852911 557513 033457 844981 258830 938676 331303 560990 921808 090956 429331 024827 120530 350006 336231 775764 167518 871227 110769 709802 715298 618656 177469 674563 710217 573093 861715 928494 832498 965814 349279 471022 612758 793969 462906 408175 028567 766598 192057 369505 993535 441894 422420 239457 468108 360963 571516 197465 451670 916553 546257 319038 512187 118667 158073 394068 246152 367931 316116 121303 144139 812163 912726 767185 458525 562083 828833 857344 284465 701240 365034 305037 537313 418785 173287 527620 110868 702701 588000 368166 153365 768609 228415 333648 882497 623062 480003 343760 876263 103717 457585 309613 181975 783090 850865 502703 593200 502239 250144 547589 795621 152100 189278 298168 078552 496734 883579 127722 827073 118526 746318 834476 396972 178926 109795 557525 458139 799913 639968 697851 050796 871707 326510 950285 705976 671542 804507 395798 152555 553175 329827 724112 043611 076466 877298 805732 261716 451245 960596 679758 792125 390641 158431 371099 590826 225400 330700 640418 181780 533171 396749 179927 500526 629167 905038 030825 079032 290529 249094 657472 842334 871068 627076 091077 701295 452732 913725 375764 602216 396552 153938 649941 177917 799911 621896 499449 468135 286823 201836 610213 353284 427058 622664 124224 697116 839136 702836 905107 760183 612789 271727 304985 006997 567281 942747 167059 304068 653325 339408 137043 600828 883339 821808 709626 403234 197128 501745 604653 830723 449435 325767 770142 962999 735982 031289 710428 925204 288512 257600 681664 146505 687055 716768 175010 892988 339742 466763 280731 652401 153487 444488 910296 636170 207458 856993 805930 331341 476679 075541 475366 307050 371438 928857 741318 505750 926496 826466 001116 654556 099097 038963 522726 405537 349217 942031 609178 936461 365958 647801 195489 151670 345426 095298 338787 320577 736331 854103 448129 959475 141093 328824 938570 726022 108784 560213 296780 783396 088474 940074 775323 972313 697493 503263 109968 995928 827013 868452 073013 309657 070646 518926 610279 648633 065201 382352 856269 452768 365100 157521 224458 680306 761509 950434 311094 379630 978154 967933 034210 431024 463991 075977 995872 443460 930433 400155 160038 986332 799675 029651 710148 144830 336301 781257 011157 324077 403710 309453 358145 260383 371797 514514 946221 095091 300202 824550 808794 087893 283658 218561 246390 990396 820003 567307 891530 437570 438473 692167 448648 317831 427943 774369 128246 161264 164889 352721 873948 930705 280826 674289 271134 241111 778938 028543 198358 491006 038734 041177 195176 569640 757196 261011 086360 258106 045717 330854 608063 441101 075537 900471 976824 464194 872851 743772 144150 329385 218343 880342 690382 280554 819167 202827 269538 200921 128317 778808 103742 746203 210302 979689 882736 117288 413349 082480 692252 308211 343832 533755 900822 295912 231278 831727 158347 917418 967823 796017 125288 776256 802454 276640 479701 369772 113461 085518 197811 682671 034123 274653 420947 988011 402771 241217 128684 699981 342703 108528 570261 473459 145763 609638 407972 091755 473750 993495 322425 889021 666321 593379 396397 384129 521550 866789 974326 975472 087753 796550 134509 305181 615997 977189 477803 860729 465568 597792 152388 225017 879354 965765 635315 980102 482007 931343 399338 094021 508166 734299 802594 745494 680563 228153 158001 390255 469061 066385 722752 634543 253817 744031 482735 974118 200196 783072 421067 427630 006470 139765 381116 828526 672834 123041 190465 726510 212736 532080 688042 715340 313443 138022 326736 343575 567255 369516 931811 078350 820071 402809 726543 262790 921652 952463 571909 001298 307149 589917 591310 945312 827007 693697 485986 292628 197130 002300 830997 535771 095210 328231 725414 976862 709054 396212 047237 999166 548310 329768 208395 289835 608773 753204 477417 838895 627790 462402 946651 565725 300786 356602 282840 993245 875858 680485 726050 347487 196830 653183 983496 329876 158333 633535 323419 062138 930452 686089 444493 497753 986878 250409 226742 872049 831878 275270 249927 654543 646103 048918 910323 201347 419185 829595 604007 456573 593584 171587 932787 584474 576560 281374 338753 225950 813567 469221 570616 246277 142569 378549 631228 891371 342562 587483 615783 812452 414186 056879 620888 465368 950926 644431 748060 217088 147456 / 2731 > 165582 [i]
- extracting embedded OOA [i] would yield OOA(165582, 1862, S16, 3, 5461), but
- m-reduction [i] would yield (121, 5582, 1862)-net in base 16, but