Best Known (8, s)-Sequences in Base 64
(8, 176)-Sequence over F64 — Constructive and digital
Digital (8, 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
(8, 584)-Sequence in Base 64 — Upper bound on s
There is no (8, 585)-sequence in base 64, because
- net from sequence [i] would yield (8, m, 586)-net in base 64 for arbitrarily large m, but
- m-reduction [i] would yield (8, 584, 586)-net in base 64, but
- extracting embedded OOA [i] would yield OA(64584, 586, S64, 576), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 41 236783 304050 876854 983742 213669 849540 893170 579001 042624 627848 751237 904251 056882 846864 048281 836332 249423 499099 648910 860866 769257 595844 413405 070881 157627 230357 043441 606649 079423 516329 953092 348732 307207 247306 727569 171763 050676 680355 424448 961011 773450 525488 101847 853289 267747 259357 178357 986514 444342 766700 150329 988803 475583 033192 862008 812829 113253 816165 337227 371154 501459 309169 615371 319137 572152 773718 001372 758641 216529 322554 036116 498836 206075 418699 854226 113809 251368 583534 003046 061330 842553 574303 019306 136654 905831 939750 844510 662138 003484 464636 588473 510441 672570 729980 674018 249744 546415 694230 217184 455717 249565 566109 254112 481212 710188 671037 678451 268773 156610 862973 214674 682344 503882 317354 714756 724324 070978 268479 475525 779467 324777 436710 858025 321031 776588 539579 609539 376287 592956 490819 691010 681413 064914 545156 570170 751676 370324 743244 309696 439335 689149 158079 234259 515875 980282 154607 997761 307966 002009 569644 821083 132164 737866 348702 221109 383494 119495 200634 576651 490568 131930 396018 520265 931092 715692 567810 384200 762391 870409 546931 495116 768013 957873 009125 073606 410240 / 577 > 64584 [i]
- extracting embedded OOA [i] would yield OA(64584, 586, S64, 576), but
- m-reduction [i] would yield (8, 584, 586)-net in base 64, but