Best Known (8, s)-Sequences in Base 256
(8, 264)-Sequence over F256 — Constructive and digital
Digital (8, 264)-sequence over F256, using
(8, 512)-Sequence over F256 — Digital
Digital (8, 512)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- K1,1 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F256 [i]
(8, 2312)-Sequence in Base 256 — Upper bound on s
There is no (8, 2313)-sequence in base 256, because
- net from sequence [i] would yield (8, m, 2314)-net in base 256 for arbitrarily large m, but
- m-reduction [i] would yield (8, 2312, 2314)-net in base 256, but
- extracting embedded OOA [i] would yield OA(2562312, 2314, S256, 2304), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 363 136381 727039 189863 516129 327916 956874 529668 049698 173115 520679 396163 752688 096506 263687 914574 640638 630850 249010 948465 534428 332783 777183 447657 575704 433761 478645 756316 294367 845923 325808 973525 451847 722947 939838 251705 519735 369996 230128 884161 719787 689249 808543 172376 554930 673813 497950 299450 940009 800356 948677 423376 282793 475165 450185 239926 874342 016631 591462 027333 688530 097243 384870 827203 475999 510103 143191 789100 542943 676958 191484 878206 250885 558119 031665 223600 982567 890118 745156 775210 993123 959204 139837 899291 273398 798562 633603 826172 536190 141819 629158 522539 598108 749342 123960 688136 303470 827583 112224 066922 693530 723401 643749 653189 443540 147632 285499 094069 485594 783368 248885 586992 463997 978304 148618 864817 257113 648607 136838 537336 888049 595226 871438 318732 401929 307781 244541 105497 527947 876255 120621 138566 387504 570219 875442 410954 263098 985696 536220 678564 651185 826857 303895 792016 825239 264347 644611 570919 265007 426700 125183 601197 332744 209754 153968 430532 722649 424346 790853 691133 228504 200071 514477 306991 331872 146769 267026 602856 097290 157034 185054 617369 840881 429004 214590 539378 306685 094535 917396 642591 674550 663075 716985 499041 171696 510833 331011 502981 017808 086677 505615 576246 806549 787399 328068 257238 311518 455190 215416 091912 120861 070727 345588 898990 599881 324352 027121 891345 878936 965620 461421 650423 045211 766422 050318 804057 559906 984642 650621 650590 163479 777050 986880 679912 611141 516290 368513 471539 269275 215449 293312 281958 145058 434039 447783 002664 112842 441461 943691 447693 835658 714072 817448 701680 535628 972102 629248 448524 148308 117329 026954 082208 947002 314635 106962 552860 009622 529621 716723 526513 705221 869072 164089 305137 566291 847402 870172 906992 584205 096554 553136 757939 199243 208792 131852 453234 985628 344110 504244 735329 337852 168433 253406 958999 792064 628766 969028 462966 506280 041238 203293 041862 280246 407747 791868 403498 066454 734857 141701 216919 605418 538458 694292 027169 819265 616284 247491 050086 746151 662372 927464 337226 354118 399474 724707 044623 248233 268402 056602 068024 524003 383103 235686 980576 718701 654663 203295 465334 867180 588296 289367 857153 747239 627295 600622 928822 609545 242069 787590 592177 558007 083531 273841 977248 470552 466942 308857 379579 708042 293839 690025 498706 936963 985155 732643 627149 289307 423191 121386 818546 357876 316437 581774 618768 913274 402912 466794 430447 928743 294227 330592 109726 323559 416374 250873 065795 731990 126333 127312 747932 954547 349498 695509 553282 411602 905407 435580 140003 508196 421924 126292 982571 301496 202697 420344 108389 607595 782365 275238 498712 768593 076411 386426 972043 406752 635286 165124 555818 214555 347622 577167 714709 511367 502802 530208 397919 662402 629783 876046 434032 535649 102866 560609 435833 464582 300742 730883 420595 864543 478248 990323 055964 427512 714242 615685 129763 588814 267172 630931 997882 122580 078775 686926 406161 983729 195284 064032 401866 379977 798632 808967 047790 821427 979721 637210 339649 530301 010234 171355 708704 755090 742499 706285 052026 557361 485984 127049 837045 542030 084793 948685 791652 476537 910511 168658 055958 992398 532380 528369 722907 680131 487291 813974 239865 254936 734925 320029 599185 216073 932967 059270 750148 486832 039471 123367 164093 682805 710485 942966 451619 730015 974324 866842 239292 234161 791983 590069 222881 102234 321385 088632 642954 045625 965721 315365 199647 399393 415805 737524 068343 645831 294558 271122 156877 213336 448285 881041 525137 743811 327335 282944 868545 616527 157524 927809 731212 780537 344671 602589 731981 648707 609281 746827 521916 199182 321024 164687 176186 845396 242829 865582 315973 228846 986697 055382 281988 464166 437916 203402 270161 262151 157104 078896 085527 721686 140503 901558 473326 226291 179032 852251 038242 247423 196074 168176 077123 273445 283370 106450 971391 250770 669189 301334 605436 488845 836500 536999 854043 876352 188196 376378 242311 067515 681233 451408 165550 325730 416274 033960 935345 429453 989961 278994 345844 085274 245683 148753 380461 629074 378639 564822 962219 117176 051756 463852 783058 976447 266641 503805 610133 493547 282914 005379 612459 315679 080852 887799 405318 345818 873306 388455 057302 702077 097083 948332 262135 415681 620640 379152 124559 363853 482691 096750 749263 917648 236613 850888 265572 725776 876450 399236 341243 660177 355284 098451 152002 672196 756833 724055 157286 286664 339803 955368 152388 156541 159816 664813 061453 226328 492388 836171 695817 644280 844574 525533 373072 974560 825565 868950 656024 260931 160259 757848 603201 083908 369857 261169 631888 821321 344193 634332 677436 734251 064953 613236 780912 083514 771192 486516 931298 573360 615651 284241 901290 755184 193706 329326 865254 763570 163313 128968 971150 510168 006528 012355 397712 539116 979332 240647 682660 222132 688053 595337 320503 506329 003388 998225 181107 189228 822212 868176 685828 033172 042582 015234 064919 899462 396202 549667 994793 136031 867436 727575 147147 570400 474462 569781 241751 558949 667217 952668 592538 227521 272041 446376 154454 507001 952938 484259 793216 619065 055330 926402 189797 408852 352545 289000 910295 148746 948400 018367 659542 089796 274983 697101 417246 522625 030531 905477 195082 097594 822887 886084 707194 556568 288791 801987 661221 117260 082009 359716 865219 494055 927637 909403 123614 763059 741206 547636 129085 633749 936349 769271 026216 083325 709363 641513 956765 158181 387502 806323 704104 202409 114965 039147 839619 344717 835991 095199 752556 114938 630480 108901 771184 326332 900335 224380 786897 763170 575906 890013 971375 047566 011629 556164 174106 832986 855352 774687 453970 704485 492676 623413 536902 785674 325308 655081 927549 589425 763323 780689 484188 394296 468415 702142 518433 287836 175821 487524 980743 855197 906704 822753 829524 320603 996417 779704 339115 594520 077744 804206 542845 350310 682706 712357 396142 704765 454802 797460 812239 721895 550102 307288 583821 538467 614329 209337 387143 675196 718599 142155 915813 914420 253012 701725 958512 058456 976865 065903 736907 555410 566901 755972 033326 322301 256228 742730 703445 929613 905340 826952 945488 494976 936627 653498 042873 546031 269153 614404 636293 017743 810139 671442 011055 780973 055630 259521 842715 820032 / 461 > 2562312 [i]
- extracting embedded OOA [i] would yield OA(2562312, 2314, S256, 2304), but
- m-reduction [i] would yield (8, 2312, 2314)-net in base 256, but