Best Known (14, s)-Sequences in Base 64
(14, 176)-Sequence over F64 — Constructive and digital
Digital (14, 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
(14, 256)-Sequence over F64 — Digital
Digital (14, 256)-sequence over F64, using
- t-expansion [i] based on 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
(14, 974)-Sequence in Base 64 — Upper bound on s
There is no (14, 975)-sequence in base 64, because
- net from sequence [i] would yield (14, m, 976)-net in base 64 for arbitrarily large m, but
- m-reduction [i] would yield (14, 974, 976)-net in base 64, but
- extracting embedded OOA [i] would yield OA(64974, 976, S64, 960), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 16966 592022 269712 575025 534652 347492 392971 206723 595564 854450 527513 742789 872861 003201 615484 657650 519696 038017 831412 578032 225157 320050 771048 747497 899476 384619 761052 077277 781678 239619 239055 485313 713521 874496 084045 279430 685797 430716 663271 282187 858338 587706 322742 489881 467050 767896 263272 164841 542075 284730 605325 488236 242115 669654 556098 915821 379696 116921 585423 116311 896150 013700 931248 471151 708302 087807 800511 857562 197463 105851 195446 684765 337033 543406 958869 198882 069145 565808 083910 945789 503996 568184 777173 604849 730763 968209 295926 114827 528554 686408 054907 647612 375961 234972 531220 577854 330364 060644 335141 070557 390977 130467 188155 545157 140763 249243 206319 449714 247218 030809 201910 904440 488943 244716 579015 911102 267032 589599 729123 965739 976773 990256 536155 679686 576734 202873 524168 520220 841091 745528 905443 214696 164814 800641 670321 654929 990589 653548 922558 297277 001315 133450 403024 641796 351371 644469 063568 756974 174122 749149 169005 003937 912957 618480 690341 466498 736975 117402 914608 499920 561734 861914 137597 434899 657695 368077 440509 614676 920162 822960 724878 475140 632705 625902 509074 640116 537621 559552 628306 107015 303863 118668 482848 823161 916421 539254 668681 661384 183862 099273 085516 192173 531503 047556 401698 876083 968566 131370 150063 561563 673950 976553 419338 833063 671891 964843 666700 701537 053576 690943 894330 749674 173852 703633 453137 763338 641972 437013 640760 338412 540626 602215 619097 912420 790510 725217 282836 756693 152196 014395 204406 288211 192921 146788 159143 401150 006613 012719 604363 432562 675033 769620 712460 539716 856896 335537 789581 833001 962616 446412 722601 078398 512954 987451 021469 816106 819254 639121 869623 009143 894167 928110 903322 853082 002022 488201 791342 971976 374988 647350 165217 866061 331307 217204 152681 656684 763843 049173 490834 850792 225267 575201 539943 684744 481872 805100 354208 261369 757434 620295 511032 210842 327380 393984 / 961 > 64974 [i]
- extracting embedded OOA [i] would yield OA(64974, 976, S64, 960), but
- m-reduction [i] would yield (14, 974, 976)-net in base 64, but