Best Known (13, s)-Sequences in Base 49
(13, 62)-Sequence over F49 — Constructive and digital
Digital (13, 62)-sequence over F49, using
(13, 91)-Sequence over F49 — Digital
Digital (13, 91)-sequence over F49, using
- t-expansion [i] based on digital (3, 91)-sequence over F49, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 3 and N(F) ≥ 92, using
(13, 699)-Sequence in Base 49 — Upper bound on s
There is no (13, 700)-sequence in base 49, because
- net from sequence [i] would yield (13, m, 701)-net in base 49 for arbitrarily large m, but
- m-reduction [i] would yield (13, 699, 701)-net in base 49, but
- extracting embedded OOA [i] would yield OA(49699, 701, S49, 686), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 68 584507 491536 259727 494724 688655 962532 519459 776333 562724 742159 641584 567734 741850 214165 006898 431088 112199 836728 757064 601260 255899 357770 152892 254946 616072 389888 602514 296136 961504 209380 220877 913760 807284 564863 582808 889755 627494 038877 393156 932262 859487 281448 044872 631272 570972 260453 556776 334244 554767 034638 573105 045132 278004 914033 156565 319364 464321 536874 179325 696035 158922 468545 375823 138008 493781 031187 535316 535881 673753 255492 092923 261809 884951 578611 309775 469595 264805 955726 162634 522003 286212 460498 549947 300552 455228 648089 517064 371181 180939 181646 208917 076534 310782 830331 072256 515678 281042 974168 611100 516756 408915 653486 640974 965173 125469 991149 829015 849720 910329 682574 199317 900913 642875 764035 976265 565137 084901 264598 064692 552170 339511 308774 662153 683706 055057 276257 493084 920871 178776 561377 635069 002956 836777 360723 264360 893456 839749 563135 913504 134641 556238 556955 106590 678211 884723 182795 696951 244011 659829 273045 401550 653783 662299 859715 858373 372962 630778 088856 431507 675192 356661 287609 917723 278460 452602 004812 922246 411009 576839 401458 186495 529630 491171 845439 860951 847516 930906 060702 774861 660749 815116 099401 237194 539530 249498 341356 649443 659598 343264 327458 798603 909217 067245 269996 058285 022964 200005 / 229 > 49699 [i]
- extracting embedded OOA [i] would yield OA(49699, 701, S49, 686), but
- m-reduction [i] would yield (13, 699, 701)-net in base 49, but