Best Known (127, s)-Sequences in Base 16
(127, 255)-Sequence over F16 — Constructive and digital
Digital (127, 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
(127, 257)-Sequence in Base 16 — Constructive
(127, 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
(127, 532)-Sequence over F16 — Digital
Digital (127, 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
(127, 1950)-Sequence in Base 16 — Upper bound on s
There is no (127, 1951)-sequence in base 16, because
- net from sequence [i] would yield (127, m, 1952)-net in base 16 for arbitrarily large m, but
- m-reduction [i] would yield (127, 5852, 1952)-net in base 16, but
- extracting embedded OOA [i] would yield OOA(165852, 1952, S16, 3, 5725), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1 077263 189504 250514 295053 131370 856594 837902 391584 896697 569458 034371 435281 387270 933438 781041 302011 117640 888415 769723 605997 001546 844697 732238 084828 429726 423924 247387 110760 812605 430515 767665 580344 210562 819395 327436 381789 657151 084010 330648 300188 653644 673883 013896 431037 771696 866174 691061 467395 380359 999918 562712 011755 774101 249241 468344 438303 587520 947524 936192 022330 404580 154676 065957 019911 355329 052302 831786 180472 389720 929023 003690 562973 650806 775310 312132 214475 591822 121891 585190 543278 558791 602907 549372 109552 030089 998729 726961 713265 627042 832689 750224 436822 259785 401530 098343 712849 878166 199967 573771 677453 722485 558593 662468 702197 710020 013994 021527 789104 097837 265765 931967 908489 568363 633310 342320 720609 866065 834119 724351 884182 398247 720081 731722 334167 136234 305524 799127 516040 019960 618986 875785 980750 742639 140984 278026 529785 200215 061988 087803 129376 580516 291909 241589 941893 500422 366058 642571 015864 441209 614232 598663 131648 498793 789401 133936 969854 320174 428699 155660 988231 402160 924777 312669 652554 001995 699500 276795 621056 524221 219766 534834 184055 536290 969234 434616 885844 587400 495092 229342 252470 984478 491416 035893 092941 224420 909985 476779 384744 507791 058060 106665 434979 422337 934653 114917 635579 566143 850251 450867 700424 800912 766029 057301 004078 334138 729474 171030 569766 945184 144592 802621 564042 871351 588511 558111 787414 418056 879801 733836 731236 671176 256314 739339 727934 575194 824383 343108 360926 085123 639587 218663 742680 300961 543895 160950 469648 200910 898680 526115 539873 902831 247416 529469 029915 196452 698230 592972 915903 777354 484241 181089 318877 905769 395299 678047 559841 196886 453812 558622 212110 965444 756315 667591 087257 606085 021467 342378 419754 258256 798026 068391 011957 498566 905884 243685 767792 019915 667658 687646 828799 670786 471472 711988 281935 421965 649637 185749 420418 336356 954697 198580 060284 673360 184671 468187 611406 958858 104850 701704 188372 602483 562962 741126 517061 670168 257242 096063 068504 651429 847353 431162 765952 040067 493336 622856 366995 207955 639405 940956 663888 936367 587570 817759 441479 802692 306391 452097 741490 316812 656537 365928 329190 591453 628838 307632 438925 736460 099476 331552 114178 158785 065075 354756 329535 202527 245111 600231 727526 033102 153046 896233 490841 708508 863163 579436 431939 948295 739615 491556 533859 047679 419003 764899 513293 214165 865732 222222 975859 563348 613301 778692 121603 530675 349019 880231 142494 815084 575585 904248 368601 467534 447211 734043 000610 828804 517682 597730 005093 443780 320815 242322 718595 006919 033519 445590 395250 282276 236580 851724 283365 239584 631228 581435 152074 652654 723362 098622 547163 946965 004762 890935 135637 820584 810855 470646 072649 440408 709594 722652 675837 117972 440315 755391 670670 031693 266956 871571 372111 193357 368286 309277 598219 415779 869518 064548 122444 337519 116115 563171 571226 710676 421967 306892 387725 314558 091154 705468 455225 020992 376660 188989 516471 933281 143994 603698 457704 309166 251783 166299 912091 610007 401196 062649 965336 386072 852860 932983 247009 583783 663889 436151 914033 183958 937739 277518 221484 419404 586610 881819 049960 279724 369989 315124 187103 253576 243443 254978 884065 715323 110484 759024 428233 234660 267921 594432 100152 876338 063898 673324 707616 919589 309016 287330 654520 924638 599070 728058 896919 772293 604442 499588 478654 654787 438117 422458 062806 565547 734484 266055 032352 958187 393816 941055 592681 733119 640671 968076 308721 216317 148170 692450 495564 426125 309207 478159 090761 111246 413267 147829 391966 994412 431007 254925 847129 812449 137897 115097 106837 374869 782833 180966 530619 130050 139449 852666 298515 905369 803386 712857 411297 011086 367533 213112 235561 623258 050922 812267 583453 080378 129246 932451 655203 569748 125913 136931 090393 174375 024277 174572 309812 015535 777592 391761 337512 485805 190758 493617 961981 228073 340042 251812 781373 884389 461125 949839 721654 447144 484981 018396 034407 561396 917579 126999 236080 754929 209343 609127 390507 377205 281235 843357 774394 136394 875552 098700 880139 621098 325611 760600 922181 454115 377401 677105 190251 762707 640205 486922 935170 893561 973297 953487 514454 171897 906791 616243 205429 746086 258191 893832 576912 721477 917192 334886 574148 456129 264502 538016 934104 707107 223260 877160 347527 786573 622015 953649 803793 642705 538591 498660 571088 069061 343052 809638 806721 119489 097212 721305 860217 208907 975004 558952 735965 701079 931585 264370 406695 266204 266198 658810 845642 326902 704704 910861 584165 344264 487433 582318 936334 768091 607818 364394 744997 816939 948116 716031 259744 818396 924551 488513 038945 501383 486564 520607 026844 341954 488685 871465 193610 182629 564350 142139 790662 065816 361044 498140 199343 128665 024157 261967 143284 677796 404341 376987 118670 144745 530398 945133 265947 479482 039713 837712 080757 389479 452806 397735 244980 299322 135294 090157 623912 467614 751291 299192 402501 414047 375117 022351 614691 126066 050924 817132 701246 824116 214025 122720 937238 051542 259799 713776 680442 016990 162078 942596 780448 442559 086986 187442 420912 220322 263626 454809 712501 063392 167732 126779 546468 488843 210912 233244 824197 298385 746815 228214 126359 854255 019283 783900 811164 502387 386624 411674 628941 381090 924160 600309 517225 402554 483895 353401 489911 974092 895642 217235 013748 064822 435251 210088 423770 045624 896830 986423 214332 142901 224721 933726 908358 175176 152450 791588 179508 357484 928313 604340 233118 109211 531162 393668 594078 352290 087951 521152 040027 594086 261318 734758 541224 027494 589393 523951 255278 857097 620868 289176 636335 180880 350902 342179 950690 605961 238701 538428 210792 449955 066289 475370 690136 318823 828147 862091 803752 463861 253424 733208 855967 153434 861821 827821 767859 017574 172429 350959 841860 740247 343532 735915 144269 636380 505699 136406 361662 178377 936603 074788 875552 181648 712158 183165 709787 390657 943329 828604 198379 769901 281312 951044 134237 912295 290224 505452 522402 868768 906767 699394 017506 008186 452359 479702 524214 893469 118920 311477 371159 440766 038148 889845 574646 602660 981737 098661 245768 923539 858020 803795 772743 830894 831925 193695 901483 083060 542471 186674 081344 123299 286094 990531 603448 306444 061191 427380 885288 651208 961860 594138 002461 849557 116372 338724 424384 887626 848419 003770 417680 951849 588554 875144 132471 497295 607671 988287 109731 947309 148382 006460 099382 907691 235407 304426 252821 521916 619011 571371 415889 010729 394219 517246 428487 843614 738546 199147 221822 856200 257206 928028 134404 007818 670866 456440 866766 240271 978226 900776 593572 921165 946610 093690 412785 109189 253000 324614 574165 221408 718512 930513 326677 451789 745452 103215 446126 230103 031905 407885 928088 321965 539882 495484 944526 660485 720879 339271 316019 107006 941223 978935 598767 418060 511335 347627 417609 511838 525031 937664 106665 929977 200407 248392 466556 528849 563730 974827 815860 647970 350917 183570 060373 525212 745373 157993 997481 456516 704793 147621 881778 178049 812570 686795 126029 296725 492653 483745 093937 167132 330882 468261 996763 003362 542501 369418 772628 503513 686306 393454 928267 995417 380772 525051 037377 250883 156465 041465 665832 740457 074787 991877 375979 126555 536714 745679 001584 208112 855376 554547 928652 594594 484595 466259 402076 239598 317397 345230 174760 453122 815295 658421 585298 433431 504894 835570 542390 347314 694115 003540 665020 985706 160733 071352 956370 112016 666153 050656 319350 247958 404552 527852 506002 794145 826552 458163 898791 962348 881159 618302 843604 792390 420582 308668 344176 695136 537932 045102 440626 425130 107392 953502 093263 703416 814406 271467 183028 050005 159845 531644 862548 328369 523323 115666 450802 699627 146422 303841 089549 119268 659493 956708 808986 851854 586169 686827 073090 854584 651759 058710 975238 998057 579570 003968 / 2863 > 165852 [i]
- extracting embedded OOA [i] would yield OOA(165852, 1952, S16, 3, 5725), but
- m-reduction [i] would yield (127, 5852, 1952)-net in base 16, but