Best Known (54, s)-Sequences in Base 16
(54, 242)-Sequence over F16 — Constructive and digital
Digital (54, 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
(54, 256)-Sequence over F16 — Digital
Digital (54, 256)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 54 and N(F) ≥ 257, using
(54, 848)-Sequence in Base 16 — Upper bound on s
There is no (54, 849)-sequence in base 16, because
- net from sequence [i] would yield (54, m, 850)-net in base 16 for arbitrarily large m, but
- m-reduction [i] would yield (54, 1697, 850)-net in base 16, but
- extracting embedded OOA [i] would yield OOA(161697, 850, S16, 2, 1643), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 374502 011805 333736 955593 212440 828429 010953 111121 887771 967706 740693 441119 609220 252475 108098 785489 688818 273053 030884 115121 538309 877584 327417 063877 690222 228424 939054 880586 149824 638034 341497 811841 943761 464262 182366 757636 097340 719630 888289 687425 446007 118481 545394 746120 755306 924053 118217 169048 885611 869127 175448 988505 791023 657772 808860 023084 055004 821782 421760 532012 964775 786278 780435 695691 201565 836424 301030 513317 578650 412847 457175 787256 325105 778399 837150 280823 002386 162393 891319 940953 915327 118401 039939 575228 669265 281488 037030 957975 648215 477991 965814 026487 819144 415725 293457 031394 445383 248060 671538 201951 018463 571488 564855 496600 704003 517214 283192 705355 161168 945179 512742 797098 355983 163643 514330 064224 886346 426016 174370 624546 436413 973752 413004 202303 541633 459850 332023 010272 919594 518985 147214 410203 205358 657274 505969 782574 138747 093935 241484 526938 173785 845418 201194 597224 450036 516799 408665 192128 571900 072016 608630 164684 114939 292996 988210 505746 442793 858097 452802 786529 183613 254929 205577 713320 232085 396284 637913 545272 760850 275206 260724 335682 953724 993103 522474 740497 415063 714081 089977 197959 321600 663595 657577 463075 178508 142437 874396 806027 054924 015129 151675 238055 624546 938931 363406 759242 342845 054223 217228 417352 091781 224098 876449 604746 987611 475087 103197 433555 371478 282168 304518 774319 130978 980231 310264 629145 527924 160130 492474 955414 334298 295914 272762 304825 862346 091067 057638 960574 040032 005321 279783 525608 156775 479897 891172 317090 675482 493182 269460 038736 366134 887472 775454 734637 878224 987711 594842 446386 689479 327966 015043 868399 353145 894851 874357 676044 258881 724114 851770 765483 904344 754725 672639 221769 727748 201805 080394 813356 075733 625048 957005 024432 369204 785567 654383 489176 925220 948253 082640 666850 280091 050488 283581 362725 988840 340392 333319 151807 051413 816346 655011 844424 418930 543421 392045 429919 703104 838568 617882 789738 485588 541465 484748 494874 097434 178907 077471 633251 874008 685950 462639 757677 839412 595808 214665 077601 469433 246681 558326 898138 291231 526051 570676 598313 037883 659721 402545 315156 250309 851848 485537 567452 708301 386222 304530 514864 834994 040377 819252 301875 904512 / 137 > 161697 [i]
- extracting embedded OOA [i] would yield OOA(161697, 850, S16, 2, 1643), but
- m-reduction [i] would yield (54, 1697, 850)-net in base 16, but