Best Known (119, s)-Sequences in Base 16
(119, 255)-Sequence over F16 — Constructive and digital
Digital (119, 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
(119, 257)-Sequence in Base 16 — Constructive
(119, 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
(119, 512)-Sequence over F16 — Digital
Digital (119, 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
(119, 1830)-Sequence in Base 16 — Upper bound on s
There is no (119, 1831)-sequence in base 16, because
- net from sequence [i] would yield (119, m, 1832)-net in base 16 for arbitrarily large m, but
- m-reduction [i] would yield (119, 5492, 1832)-net in base 16, but
- extracting embedded OOA [i] would yield OOA(165492, 1832, S16, 3, 5373), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 36091 139145 539083 352029 988220 019577 191642 943805 084479 277258 645975 417858 712457 871811 708863 210568 877264 959713 165244 928133 291051 654280 090924 958993 719466 550965 718708 618194 489707 599710 557961 642325 070538 668500 380021 739155 245445 339405 797646 757091 658953 460033 541423 580336 357749 350614 839418 388978 216520 484664 740782 102367 279705 397494 766701 734070 807701 042916 853194 610325 440773 146322 036435 396087 256195 136662 256615 200858 086860 342761 218281 944682 584167 047732 029948 632504 978391 170878 479880 787390 126530 674525 487906 376301 927777 631203 611589 394664 027456 762039 248090 716165 733038 142314 238554 443983 476233 061092 533634 551631 903495 647784 175705 123141 281545 927179 159428 927671 166766 367341 394346 591059 864775 029621 927151 123124 973096 378314 739168 746478 738724 439217 708601 166904 078411 715555 145895 634532 576914 756061 982076 832178 503449 348957 133717 639475 580536 940213 664760 289411 614159 418901 514451 331123 643241 866695 627870 689013 600221 707693 543729 071236 228319 235463 827209 862339 988750 583439 764699 020792 276245 633491 421256 023486 770638 361578 484318 753745 342894 199432 900792 337292 538211 003658 063260 482412 350096 479295 848449 794696 302138 448399 641723 212377 162955 987770 539858 631848 733688 236346 539438 036130 586399 456424 508095 551714 382802 377537 646381 947008 974692 978059 500048 439953 598256 143100 588366 311910 858933 756867 793366 935516 047562 529562 609383 948113 684111 650419 994728 494229 115604 596830 572145 083216 640562 287658 502620 550869 174241 458462 826488 886555 179015 842881 108249 639022 298123 331142 789818 947512 260021 045817 199280 814424 215808 129346 369110 075211 489168 357200 643960 748898 708457 969091 810588 475526 641556 865257 125060 502762 573754 090371 099159 551538 978472 925447 263666 518750 044403 906351 247680 751722 553527 776174 050991 354213 277548 430435 342546 676055 945004 008757 572540 489822 126354 836577 169320 549495 361229 621211 649071 262461 514677 675125 467899 528138 597991 487101 123274 764057 992066 307912 095181 394046 860354 921708 419376 338671 612229 594754 444420 283318 101894 321990 103408 335025 331229 923788 644787 377979 801855 773125 886233 124176 858913 421570 566656 260595 890310 206628 217640 265077 065030 419814 609522 770264 543327 996536 684781 712663 924596 224634 622436 121149 375201 726921 682095 868888 508696 556233 797135 615023 015748 658019 555262 369703 502562 596026 941126 976828 009800 517868 296973 400986 330831 395950 321457 283195 115964 294098 578980 838508 598478 500266 755817 104836 384377 650103 849255 921350 866987 124624 593353 738277 951519 326500 762093 029358 420520 952197 227772 735746 256527 443607 268029 743762 060888 796713 997004 155823 118977 056375 546585 516170 512475 681996 876588 802421 783889 357529 817251 104412 419450 365586 573561 978160 907089 123810 840416 874940 789324 794844 564539 710937 476658 843346 524710 444321 177039 661585 778872 923838 059927 049446 319833 617390 010155 560245 598781 855350 119307 378986 183441 963428 233256 381279 925151 363321 115569 251870 550415 853206 096441 551676 226307 840780 086756 865629 471912 199942 107906 512517 603304 212612 648646 418511 455437 707202 814899 171520 956881 712311 756736 537874 468562 114469 204123 437941 095843 236591 406393 069599 806164 146858 306944 958137 059216 652817 605894 169248 585789 198441 778138 450139 079431 602541 340531 524550 710640 585811 074316 639645 369733 701463 829620 780456 414044 005086 595847 314189 745094 145031 756225 454724 932342 019887 393935 620569 750879 148802 914788 523230 158290 914574 084294 963223 864372 850153 795851 774723 076219 846977 935441 741868 480722 334272 839993 285412 231075 639536 262519 400413 622557 927159 373907 301692 784131 422651 469775 663793 616674 129799 744427 316164 464763 756553 301275 461506 139824 424712 809684 185758 426373 422189 787748 638200 122178 498528 269454 352563 536685 945429 805868 953993 867813 260052 519943 457669 542857 052196 308067 009877 273998 744266 609207 134068 463004 324043 562558 720499 413337 263242 888611 865566 816157 908821 559178 935274 929566 807213 189587 718319 297029 268796 716048 063262 055302 178284 736084 475469 297987 819270 936743 561453 866929 563834 678646 476278 347303 715161 839879 831955 709661 835186 092592 442600 159122 109423 745563 671978 354321 366494 996550 819768 452132 324852 284706 340918 291979 569083 126575 756189 406985 310406 743111 567417 307386 559970 726749 897317 097227 197386 198283 153046 065751 163453 628793 140779 019197 110618 390367 760255 630672 453335 004013 686469 495592 657390 619125 100895 206075 878407 263335 851666 668375 258962 444507 856831 592302 431942 297399 595792 292474 810951 962705 842526 257617 313495 768993 387498 349936 478370 254468 496622 038232 982774 362423 886210 366895 848021 649118 360983 114272 101938 116498 625230 791219 345978 501508 768090 952851 647176 672089 579902 810194 969408 465834 079101 278569 353079 741684 762277 587729 207935 818597 359063 883038 863500 335683 105264 476156 828188 690689 775145 457626 887386 859729 079543 469361 216050 192148 681672 204226 534196 788812 047556 345969 114397 363569 274630 194093 063124 418454 936600 961138 775194 340939 975105 139253 274926 056427 356575 377921 224500 264590 236794 887324 654285 002197 105110 976539 343058 591681 061167 980705 309510 747309 632351 793346 431405 799067 949248 837441 907491 947739 447643 529146 109564 137192 710429 962715 230521 442308 272653 286858 357876 065959 894360 498700 474837 779453 890324 079658 987884 577643 597339 364500 218489 735123 674562 380926 650390 965119 602778 989938 249560 758407 199849 168812 741772 977284 045568 507296 943466 593454 448355 875747 030371 436620 774197 752700 702530 688871 590623 958600 937266 149405 210487 111110 357315 769659 732683 573737 407369 996975 922750 040495 263298 309085 532141 583131 261955 023276 831711 161544 307996 265154 069230 578720 034326 075546 981483 051222 949921 275995 762725 908502 113506 720385 950528 857537 572499 122009 365169 346461 862549 493391 660074 529696 606639 383448 635545 371137 346963 458359 588661 857427 500322 459305 218331 687472 659297 381699 041256 628070 780789 386721 664075 663129 488608 647629 146717 149705 329261 699129 395716 936484 964079 981956 153517 033805 693486 362668 527652 744158 675531 264914 357393 562345 047920 531339 016084 695381 290837 204167 922517 257482 970234 809304 615233 511822 805257 801927 433240 980091 535552 502263 022362 214784 667646 956084 861524 871597 532306 940959 251387 013286 013509 519573 582474 684640 707618 764604 488670 829420 257418 924477 534321 961728 974698 101500 347481 262529 198511 479105 040858 978857 662754 532368 942164 494982 481864 873744 546455 177838 988259 748728 967366 642701 867687 563561 220317 383264 589153 940060 820311 811794 716742 242672 027513 824959 086619 666101 002419 883170 699103 697867 954925 609689 555669 683462 301173 000317 527458 518824 819655 624338 305689 837092 359317 571456 565727 040260 140062 754882 877465 863624 855417 565461 668536 195677 240519 026934 491438 516465 517489 301265 420273 712864 729940 574479 161885 773658 599889 507531 713646 259258 540297 987996 880437 624681 735963 104675 551402 798358 292530 241179 998477 558143 713444 811427 387326 182453 247607 687501 670374 050046 256255 095439 434949 071052 834001 014834 460775 146428 997844 737374 723624 194878 193227 751008 671268 208244 654467 274437 332268 705440 150645 183994 652888 971659 523093 900200 055119 353830 535417 462539 256099 829416 058098 300893 748834 907869 544095 533338 068986 307838 530527 546905 733571 392840 079142 551552 / 2687 > 165492 [i]
- extracting embedded OOA [i] would yield OOA(165492, 1832, S16, 3, 5373), but
- m-reduction [i] would yield (119, 5492, 1832)-net in base 16, but