Best Known (6, s)-Sequences in Base 64
(6, 127)-Sequence over F64 — Constructive and digital
Digital (6, 127)-sequence over F64, using
- t-expansion [i] based on digital (5, 127)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 5 and N(F) ≥ 128, using
(6, 160)-Sequence over F64 — Digital
Digital (6, 160)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 6 and N(F) ≥ 161, using
(6, 454)-Sequence in Base 64 — Upper bound on s
There is no (6, 455)-sequence in base 64, because
- net from sequence [i] would yield (6, m, 456)-net in base 64 for arbitrarily large m, but
- m-reduction [i] would yield (6, 454, 456)-net in base 64, but
- extracting embedded OOA [i] would yield OA(64454, 456, S64, 448), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 5 187739 375801 385058 649188 430914 858442 588545 170047 662156 690650 827459 109334 998980 599751 644749 768133 835132 462906 246938 815557 241894 360520 749949 667422 184098 921449 707091 463071 842230 508457 189469 599313 031672 477896 482131 663167 005049 560013 954155 192310 779836 538171 880016 209856 572175 324940 022414 239103 072110 002765 210688 324582 637032 284635 391482 937606 982799 106077 325227 992530 307517 404779 557421 345308 992105 365565 557749 195239 688918 428639 161725 861097 982108 089548 450961 037729 046811 526844 288389 122469 907513 251802 479645 612774 787423 833345 921383 489843 454106 344290 870320 771777 110950 149658 763817 861174 227400 691812 386760 237817 544680 353171 392097 406700 866455 615965 025484 772344 687131 306960 996385 950822 514454 098454 835757 677094 815115 113763 995814 025134 008366 656612 028890 985966 353865 021402 826031 843278 909207 254302 808033 642176 748975 938730 814026 203468 398592 / 449 > 64454 [i]
- extracting embedded OOA [i] would yield OA(64454, 456, S64, 448), but
- m-reduction [i] would yield (6, 454, 456)-net in base 64, but