Best Known (5, s)-Sequences in Base 256
(5, 261)-Sequence over F256 — Constructive and digital
Digital (5, 261)-sequence over F256, using
(5, 320)-Sequence over F256 — Digital
Digital (5, 320)-sequence over F256, using
- t-expansion [i] based on digital (2, 320)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
(5, 1541)-Sequence in Base 256 — Upper bound on s
There is no (5, 1542)-sequence in base 256, because
- net from sequence [i] would yield (5, m, 1543)-net in base 256 for arbitrarily large m, but
- m-reduction [i] would yield (5, 1541, 1543)-net in base 256, but
- extracting embedded OOA [i] would yield OA(2561541, 1543, S256, 1536), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 2 244525 536753 530301 742471 077436 221698 966583 298271 779626 767212 346905 225896 874474 628830 299300 302883 211218 931511 503872 679043 688617 807811 719330 720796 141903 922561 155183 984011 910902 168769 774130 172707 494247 392001 599816 138638 855311 998689 951198 726199 635077 650725 261460 897872 234699 151649 138942 132267 623240 561365 603681 170655 583594 137186 426623 882939 556978 956102 434295 580431 504919 558054 626729 598703 270012 490120 181479 369687 727466 605485 695813 408899 183457 278013 853546 492904 238394 010205 149345 684012 743103 933327 106065 240427 997723 755661 218148 149412 406501 931614 833328 359626 496080 098260 036730 299033 054195 498015 829004 659760 913320 121911 052044 533262 322228 806805 637067 342631 100097 146203 392947 141456 754833 243690 203018 463169 448846 842875 414823 735451 376884 107131 185831 692331 940365 142960 278610 089639 782604 353619 673535 104867 606752 583439 006256 026651 218414 564678 201803 656201 191832 271383 352904 255513 219888 315498 894974 442433 146344 157797 597624 396620 182491 251959 034553 187213 243396 121573 741387 389412 607157 008975 483368 074696 084726 611044 703605 852535 215522 924995 353308 348824 056641 566079 365991 930065 523667 760484 540490 389299 930772 323538 451585 173492 939013 518062 819340 225373 551524 399134 738400 864414 346795 550678 109653 392839 983608 766788 249472 615083 393329 677695 498266 628773 028128 809411 779670 237396 327796 937065 062060 763574 806412 902016 438089 788464 152356 992971 374618 793387 992067 451137 880896 715843 786795 149885 760097 715489 006634 037019 621150 097752 894894 804082 388290 199213 166941 128322 972003 569936 450773 367554 414195 853589 348393 673829 548570 823617 658170 923635 301891 181935 723980 912449 050651 845163 526630 209438 605340 589572 181609 214183 503391 029036 734360 598714 589978 683504 817330 322749 984993 150623 372806 988299 196947 937501 915226 554803 064276 258775 729587 440124 808825 266707 518483 279332 638060 516413 653424 384176 692124 875766 240687 858474 815257 828036 469985 167585 763457 929865 550754 975481 030153 599350 772264 759754 290255 442809 982266 640807 252407 698823 710802 939749 801190 313841 411268 735496 119017 208411 770534 475863 617893 002348 531511 386737 203067 611613 485267 365658 543963 771538 887046 632632 640870 088225 906287 036390 996919 709338 813300 104181 881631 369230 063442 412754 060561 545304 204536 538318 304420 519264 973708 683390 927989 582578 307909 120379 887593 511586 772057 557678 942246 075603 976058 376731 875494 582416 779107 886481 890007 624660 523735 914356 398452 905894 333193 113325 260259 122914 658285 734995 402253 328044 260513 540300 831979 104408 919112 808281 181843 724285 512284 084503 068938 377638 483128 845373 466535 530985 331260 313669 670848 012545 645464 958852 146919 673858 983676 992458 290505 369549 276726 143934 802889 028785 847996 443376 565823 955935 020909 098422 156699 911557 391988 618473 291495 365741 852085 158261 670668 725423 439213 687246 267076 562533 605225 492687 962295 438896 130897 300515 305913 819759 389326 323949 607751 899786 743204 806596 080264 347164 762150 348822 992104 953148 629636 638854 385707 143010 350808 875249 452905 837799 023637 250320 770249 195348 767575 365000 090603 205098 314148 321811 690136 325622 713194 442616 853561 434227 894079 993308 665146 831234 692103 616154 215777 802265 927083 469801 908992 090440 783186 156504 536913 706207 099298 494472 495842 262977 507797 582991 949094 836473 521745 374783 424220 813770 126740 530835 359783 397312 424850 488310 547604 399085 515193 896390 242441 083115 039529 835324 057706 643541 364668 498011 716122 222616 561237 393328 561509 845299 450944 518018 885603 261414 698005 449006 672920 123365 947759 394287 671489 314850 318249 892388 619761 424673 375695 879315 775419 970213 439678 434131 227806 625804 331884 371948 605240 735626 545737 127733 611007 460452 109585 424699 607125 549243 638100 135319 987572 054629 039343 235464 658745 165551 055716 436686 297606 892387 499109 981015 421199 998400 815677 475593 919898 829054 721858 009207 439220 519140 116104 176719 592419 456527 631598 172470 711584 203722 042666 570435 803757 437897 372095 484354 691773 641927 178000 362364 874045 745071 069925 645637 239856 796868 899583 898159 153152 / 1537 > 2561541 [i]
- extracting embedded OOA [i] would yield OA(2561541, 1543, S256, 1536), but
- m-reduction [i] would yield (5, 1541, 1543)-net in base 256, but