Best Known (12, s)-Sequences in Base 64
(12, 176)-Sequence over F64 — Constructive and digital
Digital (12, 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
(12, 256)-Sequence over F64 — Digital
Digital (12, 256)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 12 and N(F) ≥ 257, using
(12, 844)-Sequence in Base 64 — Upper bound on s
There is no (12, 845)-sequence in base 64, because
- net from sequence [i] would yield (12, m, 846)-net in base 64 for arbitrarily large m, but
- m-reduction [i] would yield (12, 844, 846)-net in base 64, but
- extracting embedded OOA [i] would yield OA(64844, 846, S64, 832), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 333 509348 536679 373053 606877 241488 869985 044391 715029 248228 430228 361076 568021 074394 778474 998277 625332 523885 303824 821148 813491 336350 156054 233463 999272 141385 767874 393817 493200 611170 637395 076645 409091 761716 129413 831031 155057 959773 706418 435353 460334 435097 813673 718346 209238 253705 953895 157367 011537 641201 240329 744154 406290 964878 622152 113093 630930 773570 284013 254106 961742 920075 461737 531607 785769 370094 190211 427287 529744 892886 910660 807098 998543 241205 557580 089661 139728 292275 752248 146207 762205 750564 567437 600657 552579 290519 284175 465037 145943 771892 192358 766547 415896 319199 783733 401598 287482 426732 808201 819288 047242 204442 802389 406245 595023 973179 897887 657140 995925 181643 417714 310307 744705 636657 374902 002315 025097 030116 693117 087742 349747 945688 821241 924194 445125 686202 866113 927214 987747 291336 236350 111235 666140 530178 203502 800818 433524 810063 989538 056739 083529 815259 875303 604208 753644 923017 874977 425495 125495 246397 545815 607836 579350 796831 781610 156296 744598 271445 362552 656681 796306 957977 839200 905764 743746 821160 817138 181197 289419 008944 453374 131889 367975 967013 461071 284366 723259 453335 296104 907407 854986 953594 255894 472154 931863 561924 449899 026343 037633 061976 609407 197890 920344 086928 253736 135166 352020 088535 450031 417336 962209 523967 590257 144423 388910 906130 859478 684894 081734 307988 021217 089468 773732 294870 687068 234472 862936 444771 690213 484906 352750 990865 771442 141612 333473 126996 830510 344438 887181 212167 192789 284728 682265 560198 835977 949664 601349 098493 814214 778154 240373 249915 057519 197090 403197 078560 245998 159525 577018 165996 734729 400681 672950 766893 006848 / 119 > 64844 [i]
- extracting embedded OOA [i] would yield OA(64844, 846, S64, 832), but
- m-reduction [i] would yield (12, 844, 846)-net in base 64, but