Best Known (258, s)-Sequences in Base 4
(258, 257)-Sequence over F4 — Constructive and digital
Digital (258, 257)-sequence over F4, using
- t-expansion [i] based on digital (225, 257)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 225 and N(F) ≥ 258, using
- T8 from the second tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 225 and N(F) ≥ 258, using
(258, 320)-Sequence over F4 — Digital
Digital (258, 320)-sequence over F4, using
- t-expansion [i] based on digital (257, 320)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 257 and N(F) ≥ 321, using
(258, 791)-Sequence in Base 4 — Upper bound on s
There is no (258, 792)-sequence in base 4, because
- net from sequence [i] would yield (258, m, 793)-net in base 4 for arbitrarily large m, but
- m-reduction [i] would yield (258, 3959, 793)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(43959, 793, S4, 5, 3701), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 26375 562312 192494 575006 331857 249355 117524 561939 916513 972715 929238 381426 035616 479398 136269 762086 337898 167600 762367 522545 664591 825188 644924 477921 235813 212615 322393 663293 091974 263666 801650 520386 969665 246970 841219 903352 122751 682469 305699 304761 978694 330528 129860 844156 018373 580516 685631 749352 450304 929148 407362 816135 010141 006230 707584 477476 797931 965450 082574 121583 175645 947476 249884 587937 664719 815843 869878 825715 106298 239584 046287 613577 278212 063803 214622 303452 977445 851570 251251 738733 021672 899899 840823 086305 366848 289636 165100 559203 496496 169441 066884 100690 249390 616321 759866 378425 030349 175895 877338 129189 764634 987986 840240 956059 365324 988331 070078 412662 546290 615906 362162 636328 312075 596097 576207 270698 087816 920220 166093 798298 763458 287640 967369 390205 683601 444306 822350 951748 025029 013101 589706 890811 302350 718333 219331 387955 068660 963841 341974 633356 168522 147231 343206 089217 046549 840800 148744 707780 624358 072672 318041 198262 899144 664869 109267 613268 916438 885372 073528 073045 362408 213807 397708 432723 427408 535849 726468 218729 754168 371171 972183 927939 410694 712500 872365 147629 885964 880723 606677 640418 581715 705823 281965 913041 628718 455794 990371 491842 525869 028376 881947 561729 086876 010230 427870 665134 024704 833019 230378 136067 165421 582031 538155 607983 836581 432059 854401 477874 668830 751502 230730 499647 054909 476593 406168 526223 393204 422046 928497 298718 161605 558359 813385 303595 308111 155607 028836 322215 566773 266359 529452 142110 254691 687131 808312 204890 157559 181378 244828 948126 063943 601614 515742 861684 619412 011399 214526 771862 039085 795738 601859 568864 500628 134549 835209 158697 323770 350992 845629 090217 758126 461528 808975 710034 728291 034258 062659 681167 063957 186126 365336 866313 334936 600637 034753 787676 770856 534067 841756 096163 938528 153551 770744 826727 865564 302814 796950 917496 542711 962938 888482 696018 974293 811045 218184 727196 618503 243849 940768 925986 170661 674829 657473 853871 352833 255532 459398 876183 597838 458719 282448 228598 041611 285136 315579 429667 119368 592890 667031 823622 347660 858936 412012 099451 748815 600037 416966 802669 199232 213809 503711 426670 596741 630304 658972 444169 983470 405374 226483 682834 587258 583581 347672 720021 961676 968139 669924 035713 024850 662995 015510 021298 759801 062970 190403 444885 359860 026582 948972 064649 792248 384006 317353 178668 202001 062388 428416 398570 980239 104867 592365 034430 510426 572599 904862 495942 459983 216463 425732 166234 098355 007456 085018 804493 634043 846120 352751 164944 918158 884116 800530 552958 977639 667764 662063 726734 852222 877696 / 617 > 43959 [i]
- extracting embedded OOA [i] would yield OOA(43959, 793, S4, 5, 3701), but
- m-reduction [i] would yield (258, 3959, 793)-net in base 4, but