Best Known (22, s)-Sequences in Base 64
(22, 176)-Sequence over F64 — Constructive and digital
Digital (22, 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
(22, 341)-Sequence over F64 — Digital
Digital (22, 341)-sequence over F64, using
- t-expansion [i] based on digital (20, 341)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 20 and N(F) ≥ 342, using
(22, 1494)-Sequence in Base 64 — Upper bound on s
There is no (22, 1495)-sequence in base 64, because
- net from sequence [i] would yield (22, m, 1496)-net in base 64 for arbitrarily large m, but
- m-reduction [i] would yield (22, 1494, 1496)-net in base 64, but
- extracting embedded OOA [i] would yield OA(641494, 1496, S64, 1472), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 13 872383 710760 227367 666713 501835 359679 301685 702950 985358 367187 942066 650035 586029 065682 864829 182073 322596 269672 552086 792353 928237 041084 698860 930570 293773 446574 045778 426458 459196 747005 754442 325700 926146 629167 731794 859135 156459 503671 326272 782553 726045 808491 902169 666250 896285 930063 459195 304896 425661 669688 201575 306526 022601 754997 715126 352699 914667 603200 332086 415666 625122 672670 464167 070736 083524 252987 990650 855417 572797 758653 716701 136925 899006 990210 788880 775722 616638 230914 327428 230245 046044 540690 081049 286478 408355 087085 299450 634950 575229 103620 649333 084533 422705 533312 523629 931261 026815 880244 640329 727919 006867 055938 783278 027717 883842 663889 876901 017232 303732 160139 667090 181551 317238 503103 624649 694746 474005 236261 224188 851484 467404 046164 352692 308943 938444 936463 939251 822176 077355 052768 124893 472398 068706 003150 988742 970737 440977 535162 480206 124106 548785 007707 188313 636476 041972 864300 258059 470817 607781 458377 654638 613689 441055 759357 907041 207064 845376 704049 622800 533081 577884 474563 490258 550719 240829 311618 997974 313076 474693 158204 879329 545604 095563 034466 193609 632124 526524 800790 517001 768815 282101 865174 834548 988101 535798 182365 070867 021676 362806 509681 832370 389078 473309 788894 232867 298951 663953 942508 643431 472062 983236 445042 260261 570786 144293 048570 889800 066027 241078 837982 221140 217205 026902 483876 178402 176889 716372 993384 175139 564838 813559 887708 169295 283925 161574 301196 920103 176575 454558 470497 552335 483263 625597 079224 875309 087179 381479 833846 574703 931584 212717 537719 663465 152856 768118 204966 555129 082498 716750 868009 665707 120938 942983 562603 430767 916168 294570 029684 609740 440611 677877 651282 040121 109747 370608 769488 568230 097516 843372 409551 355372 025571 059538 688920 434285 979578 962336 487886 603955 050682 346404 760003 285581 650363 362481 749134 415075 423584 009624 208856 760764 112096 081078 904656 455952 254389 188524 084051 958791 246432 431379 291847 164333 192215 630871 815097 750338 630416 769780 175992 493158 979040 904100 359434 282321 017129 673884 956887 636320 799821 296794 659340 605641 122528 798239 163506 492910 540419 600980 256412 898595 202660 142716 879887 218182 855963 617532 708504 522637 103084 986109 518995 950899 329873 408999 084188 386489 585619 272424 972731 866811 240837 277078 004317 193692 422046 850052 747294 660710 963809 008130 597142 969654 409110 820094 651393 133841 377807 044976 046626 707236 507162 131427 845920 435102 138239 657201 827471 308762 603446 109913 743318 681583 948422 227930 358072 686434 948031 647868 240492 106465 619820 417402 747321 208061 093577 528791 411176 000314 998890 477012 668762 111731 385662 355530 508788 609411 687219 646530 585908 133447 096990 372266 388778 597991 082393 787216 206365 444039 113698 933061 283565 263644 152361 751128 974329 368332 411982 513487 653172 506222 276940 815818 104054 866691 973597 945973 423355 982794 693866 452876 936238 316548 285327 027264 040461 185509 018042 775887 675392 / 491 > 641494 [i]
- extracting embedded OOA [i] would yield OA(641494, 1496, S64, 1472), but
- m-reduction [i] would yield (22, 1494, 1496)-net in base 64, but