Best Known (26, s)-Sequences in Base 49
(26, 343)-Sequence over F49 — Constructive and digital
Digital (26, 343)-sequence over F49, using
- t-expansion [i] based on digital (21, 343)-sequence over F49, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 21 and N(F) ≥ 344, using
- the Hermitian function field over F49 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 21 and N(F) ≥ 344, using
(26, 1344)-Sequence in Base 49 — Upper bound on s
There is no (26, 1345)-sequence in base 49, because
- net from sequence [i] would yield (26, m, 1346)-net in base 49 for arbitrarily large m, but
- m-reduction [i] would yield (26, 2689, 1346)-net in base 49, but
- extracting embedded OOA [i] would yield OOA(492689, 1346, S49, 2, 2663), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 42408 730948 994554 094415 753201 235383 178780 090333 209104 321503 914121 204316 566207 472502 849952 944046 207901 514172 298221 533664 575652 231005 342558 362628 857899 963004 343861 487322 550957 720605 805696 205007 593683 586859 005375 083897 675654 942207 003725 574806 634656 055408 543556 170148 129957 635259 957005 925243 197354 547166 310594 201249 645499 965785 371329 666781 813611 015279 358694 500949 687510 936563 142380 017419 806497 374134 150413 919774 691859 719407 728314 431262 776443 357933 537844 125832 095381 193207 365593 712598 766251 052156 651130 914998 866290 365697 770078 901508 744962 576533 378163 973780 309236 928884 150453 394585 666208 294196 044808 712431 614733 582754 936763 595263 022576 537867 706896 370510 764111 448200 740512 099396 123912 988514 331874 580584 715564 312435 619498 293055 328713 828471 587846 342253 468843 250104 697841 643445 285103 812550 452342 276803 761304 375875 544587 810999 666234 288661 788249 374835 539919 894314 572481 600500 147501 549226 706506 993480 639987 495842 948195 608252 366178 670435 463857 679837 267820 996595 462496 506470 861214 768174 683124 723644 834410 437584 882703 125364 902428 508523 035964 722624 949778 806045 029421 845485 253926 308717 085527 852453 910062 500389 270172 376941 050832 294053 152457 213673 981811 012147 194926 057884 459109 140258 030110 560694 154606 449407 271848 561979 816070 206457 651061 914309 820293 249613 975632 231456 304236 389616 422515 509646 788960 211355 519041 016410 107521 205271 410333 824134 602617 113303 042376 299060 326263 903649 579945 821297 019159 560380 322882 378276 137091 968644 073709 566322 748985 680073 965295 294437 058571 171309 453313 191313 576833 164537 063352 328712 971478 649741 061650 445370 875955 612402 260932 929069 832241 700290 769497 282333 534996 951304 402196 960102 640463 908937 356517 318765 599821 401738 686303 513691 910522 461797 070175 570614 534187 101953 801156 881077 209999 503240 367608 826833 273461 635070 024109 390364 782942 362758 972724 875367 491727 408120 899448 035931 159744 335481 823285 635604 454986 368767 591496 471977 650483 238136 739805 920274 906010 828939 159329 090721 970397 139032 254561 077249 722400 991750 458630 885837 674241 949103 771615 847300 389751 990146 430661 891354 856776 152567 833965 222697 304091 251905 758838 219016 926432 209501 774039 770281 018863 532912 844998 277479 558716 129907 600524 596656 820445 198075 166309 914485 660396 479623 224008 379430 835661 603367 455093 098584 792369 584639 616120 320664 895028 361831 098487 057688 731456 203913 018259 188429 516349 102161 972578 880443 766280 329476 543973 328593 026829 749792 314137 611099 970785 422144 050879 844945 139993 160117 842025 616194 638226 003639 481933 728816 398497 026112 204662 316958 868964 532994 729560 805234 938182 424305 531280 515581 032731 727630 441370 989006 126471 449476 137701 657782 028816 120513 679763 223804 900830 359764 919668 302068 361369 428292 409831 598455 732495 053916 775499 597387 046545 345143 076530 263360 206835 328812 455474 638003 702705 379361 482682 215484 317960 737824 016483 336833 713812 052809 108446 423319 005838 990482 624045 958104 613014 879816 846049 594768 010416 304429 146481 045440 740537 555737 709375 573594 992222 165765 804525 716339 713252 229816 422854 777287 151414 812015 759077 403989 285667 093516 483749 343516 438637 360228 836099 381261 067927 919329 146516 159274 655486 138897 458477 835403 155040 392660 116772 482248 110672 261295 813093 787422 698224 477817 371005 975432 055551 805321 286817 201808 288839 189612 017158 553014 590070 008538 147264 589018 809364 073402 233459 400449 066020 585329 065371 602730 860434 876801 875313 094804 722724 173734 496697 823943 914817 859543 049199 438755 946931 253295 332291 461032 294664 265282 775956 204158 465872 482689 210032 517674 540248 537702 458464 541971 767763 624792 472408 757018 776147 443253 373443 153643 046886 624067 323837 035621 209465 180394 580391 816544 627242 976110 674991 582841 658328 025684 793475 220063 417138 094126 817616 173264 660124 396993 468928 671452 685472 020408 795002 622206 221401 494000 248429 842486 315956 827455 660199 727664 649122 075567 734703 274811 465970 479692 857271 416750 991217 109732 300279 114212 498034 267728 453465 704873 979709 227406 865729 425114 886884 127353 939033 289842 556824 376357 958678 451194 930272 855134 988011 910304 201910 957242 212175 290397 700388 428173 263856 961458 574929 081067 084340 041296 648619 431443 626050 030883 758387 649184 213459 184782 945524 393371 687115 811898 359956 386585 247832 895196 300692 798563 472714 729847 802750 868694 453699 707302 076119 186434 493771 129417 780326 556531 216601 291922 708632 059007 948310 258501 992820 767317 568059 107696 106319 312649 532062 268370 760897 030299 115544 197539 774078 353944 087437 036281 433537 305598 522083 930736 548094 611733 262004 400675 932872 226259 751017 868032 116894 538936 466497 539803 956620 423016 052282 070245 029461 558710 612505 982746 954370 938544 179663 307151 092055 050641 334114 852347 963660 956019 196290 080328 337899 229977 952271 885749 431721 453442 195239 100880 815971 296146 281380 794437 631182 711815 476802 028964 075381 553147 696495 334170 600449 316225 662622 093731 967081 628001 / 37 > 492689 [i]
- extracting embedded OOA [i] would yield OOA(492689, 1346, S49, 2, 2663), but
- m-reduction [i] would yield (26, 2689, 1346)-net in base 49, but