Best Known (26, 26+∞, s)-Nets in Base 64
(26, 26+∞, 177)-Net over F64 — Constructive and digital
Digital (26, m, 177)-net over F64 for arbitrarily large m, using
- net from sequence [i] based on digital (26, 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
- t-expansion [i] based on digital (7, 176)-sequence over F64, using
(26, 26+∞, 425)-Net over F64 — Digital
Digital (26, m, 425)-net over F64 for arbitrarily large m, using
- net from sequence [i] based on digital (26, 424)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 26 and N(F) ≥ 425, using
(26, 26+∞, 1755)-Net in Base 64 — Upper bound on s
There is no (26, m, 1756)-net in base 64 for arbitrarily large m, because
- m-reduction [i] would yield (26, 1754, 1756)-net in base 64, but
- extracting embedded OOA [i] would yield OA(641754, 1756, S64, 1728), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 280 488030 547474 663109 467976 988045 585255 262161 644310 895781 303790 331389 453811 927413 069197 502613 860697 911582 715267 278527 888650 635236 291549 570737 213196 747511 345078 990901 595558 633710 338976 341984 659714 076087 595174 341602 553536 439143 395783 601161 977971 151852 888000 365830 912148 649915 623382 691323 549121 775986 714888 801607 073669 723811 867829 448972 076089 253756 762120 843495 876146 482162 370647 867443 987192 759973 455192 039399 425643 048462 654456 864794 323719 096635 348494 358910 902668 868788 484933 202672 221400 533174 473324 617163 536769 681087 411220 925013 583268 682465 307637 040583 708913 940470 336517 361455 478795 891155 908486 827608 680213 200740 337132 167540 344991 144674 546226 304539 555255 645829 036961 711695 918221 718416 905443 981155 496141 919435 879808 389609 254423 368715 873623 809368 031749 664528 157533 358894 372724 466581 802932 545488 616603 874232 678563 621980 977824 750994 846137 872090 340797 871875 182163 397868 529596 269199 275936 925180 292627 954063 323393 076364 986253 416210 429726 647265 633467 630139 686548 728544 632023 715768 512282 634073 663176 173539 544597 784232 467467 020213 994956 162190 094482 387077 663576 942129 394870 095750 619738 139540 030880 684535 149263 484684 759275 212044 073933 232477 027852 750236 779533 582902 934558 497526 052406 349732 635630 193535 106197 171511 871911 794008 460358 301593 805501 829480 830889 117507 818639 357341 812982 002731 412425 410945 367539 912465 333097 442737 558650 068896 604298 201124 513480 644870 262838 870241 582743 008516 808253 828601 001449 986402 195638 824041 337996 375638 473319 626999 765198 417867 058437 170020 590853 962255 174578 894678 528449 142796 837045 750214 798635 992196 620843 861492 964015 856928 638825 643265 924921 681873 720491 211784 648872 225056 497500 646066 340884 850538 988915 451537 307315 416794 608071 586015 310489 256011 917663 372104 435818 767348 079554 523574 365629 050409 387393 239713 458132 333943 361650 029813 950812 198696 289558 801048 250015 698333 966787 690861 492274 132588 068992 629158 501374 008757 121622 807952 915871 431037 753752 307030 096881 115187 812956 861732 070009 662174 148862 200314 232773 780764 889261 296320 175476 821474 589397 781897 037974 943546 038293 282078 411037 951679 199659 461060 647227 944022 970128 364752 242392 999930 971013 365234 058471 876514 210437 868317 032801 913736 064193 356894 674170 699215 625992 259791 644928 076520 532766 944165 364857 157041 236374 516623 707946 669436 143761 360001 561532 191206 441388 361882 073978 553344 941777 881145 701198 058671 646292 114701 197414 983283 262617 829950 275790 117456 252261 095662 537941 184446 596878 741066 485167 751092 029045 180062 910978 494039 625198 103324 612151 440928 027327 876637 244157 178690 785868 878713 837580 333984 737249 303355 791575 116564 485748 993768 645521 001180 382424 636207 409179 529604 802211 896788 523704 226661 945366 388622 608973 817460 486364 303722 389765 583367 872330 028020 275611 950903 666516 693532 273743 565789 655661 515427 680395 927221 154398 741287 073438 100096 011669 380659 390031 971802 921667 457141 048291 847680 194770 363632 454949 634146 530810 402966 804924 243497 163471 007589 490160 055183 132142 300017 549274 252895 542399 813521 226360 203179 922639 630942 427316 470465 439820 834323 891154 852795 073936 514660 244019 216782 714526 858114 682355 108086 494614 292920 838181 455085 827975 916247 511652 351498 647866 456138 245438 962122 144029 229160 052716 876356 980790 615295 501356 502178 671087 559817 066258 659177 829232 145125 422783 262488 945972 975877 107971 617441 300196 686940 333017 854478 647296 / 247 > 641754 [i]
- extracting embedded OOA [i] would yield OA(641754, 1756, S64, 1728), but