Best Known (15, s)-Sequences in Base 64
(15, 176)-Sequence over F64 — Constructive and digital
Digital (15, 176)-sequence over F64, using
- t-expansion [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
(15, 257)-Sequence over F64 — Digital
Digital (15, 257)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 15 and N(F) ≥ 258, using
(15, 1039)-Sequence in Base 64 — Upper bound on s
There is no (15, 1040)-sequence in base 64, because
- net from sequence [i] would yield (15, m, 1041)-net in base 64 for arbitrarily large m, but
- m-reduction [i] would yield (15, 1039, 1041)-net in base 64, but
- extracting embedded OOA [i] would yield OA(641039, 1041, S64, 1024), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 45 459207 951535 447984 980402 273584 157837 281959 658144 774722 357566 863628 093454 162501 230177 004908 984497 435772 654222 894896 421208 128775 061240 551573 909126 395306 952711 857453 741163 541576 403142 338099 299897 829340 560038 947717 802704 805709 370639 397432 151812 664914 189656 782276 818171 119228 844392 602718 527457 449707 918184 617288 939043 417764 947528 616366 113560 853854 344336 909457 744727 823686 591789 539993 622947 065364 033666 464370 354837 665539 248229 451761 088637 764839 945749 714210 075319 110195 225508 554920 842241 605285 757036 317080 374564 894291 511257 027275 578164 657321 188938 641695 680579 966737 405363 237716 152538 108039 560364 687580 511237 871704 864489 061047 526596 745969 132905 706777 480263 917093 907678 107012 974923 203240 386967 852230 654679 458275 133437 864281 123952 669837 399170 535503 454073 572398 999851 393651 567789 120893 738733 550128 377215 676647 032022 539361 286795 964463 748006 416213 710561 718710 007146 358685 191214 527206 229186 215510 736696 797812 160894 695734 351607 071103 837854 554105 698292 501442 436969 287154 441538 173650 191467 593481 607762 649613 243815 484159 848302 468827 337211 114813 737783 645317 384218 481801 391183 944247 842452 518517 871025 970145 219653 872099 707501 354160 235235 566234 496118 043309 467636 898665 813008 004672 087949 337876 376739 131634 369430 284269 365470 716451 579003 820227 494629 830595 213993 465454 976346 548425 857957 913377 671566 589079 849810 575439 620269 883411 430498 523752 527724 817968 223286 722317 855269 731925 636668 094992 009941 145798 518269 466602 011816 725233 167510 400487 370206 423333 525307 418695 981431 249342 700003 017050 851410 213300 410868 567215 753823 850650 899464 697725 255234 870619 917518 398692 195342 245372 829067 555865 753334 707762 482356 241398 789054 929350 994187 890191 026226 062750 681492 111130 573946 881520 155361 388219 145421 553262 933864 796857 958978 316041 680370 380393 504131 788154 725785 129985 270231 344924 293582 342483 072104 574472 295185 381318 903729 903272 841568 202160 539353 384496 131391 858048 545336 809294 859960 310114 625977 249583 477489 248289 748200 456192 / 1025 > 641039 [i]
- extracting embedded OOA [i] would yield OA(641039, 1041, S64, 1024), but
- m-reduction [i] would yield (15, 1039, 1041)-net in base 64, but