Best Known (55, s)-Sequences in Base 16
(55, 242)-Sequence over F16 — Constructive and digital
Digital (55, 242)-sequence over F16, using
- t-expansion [i] based on digital (48, 242)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 48 and N(F) ≥ 243, using
(55, 272)-Sequence over F16 — Digital
Digital (55, 272)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 55 and N(F) ≥ 273, using
(55, 863)-Sequence in Base 16 — Upper bound on s
There is no (55, 864)-sequence in base 16, because
- net from sequence [i] would yield (55, m, 865)-net in base 16 for arbitrarily large m, but
- m-reduction [i] would yield (55, 1727, 865)-net in base 16, but
- extracting embedded OOA [i] would yield OOA(161727, 865, S16, 2, 1672), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 5 921182 854562 606459 864465 588564 152488 077651 000127 552108 711928 459887 955060 300796 761815 538993 460116 666961 008254 057384 316512 546391 199515 346927 003978 558073 354588 284952 762625 991559 978083 871058 900827 047195 541301 372695 910848 509634 394001 381543 907781 904119 697456 898514 362677 787368 571628 849914 932361 320458 841602 607885 904070 228666 729216 007143 182540 410414 286304 304625 412074 892395 992662 885048 818449 883362 385395 481623 413692 214637 803900 479605 350880 347595 345125 330478 656121 411378 101459 673573 004452 266997 299474 943214 669879 320695 736534 327981 491827 900229 415285 660579 468243 298008 992396 584480 755064 387568 338245 413694 619474 857090 827714 356559 388383 348580 561901 544904 632205 226504 947680 038979 836424 450568 967844 538477 798912 777294 440005 277034 217826 028614 818350 175700 907861 827345 090498 053032 646355 469821 469570 761679 725889 432215 610749 971318 128927 817439 022820 151976 402176 816386 406611 701170 423227 416037 108577 744526 916143 840966 290031 082340 143164 763269 162363 627702 088575 966428 589357 622220 443056 370956 731193 608783 032453 464637 884317 820053 017920 329308 427513 472390 336715 673281 794789 468340 049798 108473 370290 668041 141750 584913 080878 956205 149370 270705 183527 194592 454246 925704 627932 922848 237341 007016 812410 606174 528608 829639 932198 105441 676140 655051 182428 517358 196639 868047 112744 018062 465488 002188 305128 663490 877171 543700 481419 541210 920678 299460 250813 930257 137723 997443 940526 642344 897288 562687 493645 631711 640632 829216 534389 900623 959613 164559 548810 058885 583337 995777 339557 083181 581639 348409 945569 930329 074028 637468 642933 201820 645394 011184 498199 422118 355424 655802 923843 150918 132883 457033 454848 923370 355739 171006 580911 595520 025962 685052 652454 228730 332419 503246 689573 595178 760510 480313 799535 831536 455060 175530 854064 006654 335327 778047 308187 978396 564864 221702 229289 860667 162818 123376 952289 744759 318027 660193 960544 930364 924331 043976 135054 492051 290420 275692 376028 672346 952764 226024 992242 992125 046690 109782 128469 668410 188852 415510 831041 902430 563718 244772 318630 227356 512941 217815 582616 823503 186387 574180 919760 257184 526307 279658 717810 438732 210871 727242 257327 047931 759529 149952 598821 779321 647273 933760 479831 232044 575954 240036 503025 614848 / 1673 > 161727 [i]
- extracting embedded OOA [i] would yield OOA(161727, 865, S16, 2, 1672), but
- m-reduction [i] would yield (55, 1727, 865)-net in base 16, but