Information on Result #1877100
There is no digital (31, 1585)-sequence over F49 (for arbitrarily large k), because logical equivalence would yield (31, 1585)-sequence in base 49, but
- net from sequence [i] would yield (31, m, 1586)-net in base 49 for arbitrarily large m, but
- m-reduction [i] would yield (31, 3169, 1586)-net in base 49, but
- extracting embedded OOA [i] would yield OOA(493169, 1586, S49, 2, 3138), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 55 930473 122095 544331 838236 782987 779669 088475 207083 120293 359048 104101 361656 563121 143592 065561 574443 127402 837618 738935 132341 079250 298366 663269 167793 456987 415859 170950 787860 813645 029294 380635 563932 048966 505104 975601 787281 745842 799921 640303 799334 308023 419004 862160 784138 397420 919872 162103 914087 292478 672793 477848 468342 232033 784082 406304 618524 288056 537371 402757 813695 995946 140564 017764 222467 727083 659253 310795 710403 793448 063731 200373 014506 326014 193120 927428 508798 672507 967878 358141 155823 653978 864300 871410 728928 554657 411461 650930 113058 442854 316650 635464 256191 880522 067119 055715 548143 547414 362284 492188 695427 161916 304102 134510 243913 809013 401061 334252 089289 775142 323309 516201 340454 919343 780325 427771 265846 871650 161089 050341 951377 601562 717590 951143 827470 675319 469076 634682 489964 864099 971973 810275 468018 335276 802341 336526 861783 561994 975790 353401 659021 207946 336833 967872 207324 098791 176987 464932 588545 019842 943703 399486 790049 422535 779439 269755 076041 320311 236816 793237 469825 293144 015816 018641 503728 677387 727239 964586 864715 882163 914941 175216 157308 384651 948599 935029 219224 510354 972252 914026 275435 494107 472905 717943 395249 864866 467645 232506 451963 901939 947074 335057 390948 117840 007881 474340 023651 592976 945864 924476 610725 697229 374328 269268 926582 901648 913623 667010 000188 484077 673074 353189 699854 831151 389018 988048 738972 624130 543355 354266 634171 288642 336449 935983 300244 683616 261524 037552 876047 964998 557502 692966 311664 855181 638429 110143 137109 870570 540752 532722 605188 528347 170641 112337 405639 317448 773397 857153 144825 672026 924577 265392 183968 618994 229549 826233 195035 178616 144457 808666 937577 788601 517910 860663 274450 969345 643450 031478 935916 494635 259315 940037 557113 639529 951773 389417 558277 035947 466815 563590 448078 250837 654646 270118 723325 279302 380454 673563 743559 013615 176337 302942 099229 768635 001437 403224 252649 601761 134462 438885 484731 108621 493783 469287 893338 385374 076293 637904 597484 159172 973091 691798 315120 419145 523192 145829 408573 972849 771280 836412 685430 959546 700958 591459 269777 047576 837593 296044 962932 483534 678378 932314 241264 922504 016722 826388 197868 588741 715001 896643 261315 734460 597158 044030 868039 353017 993461 142878 895288 351246 339181 755053 299881 098729 540478 859442 933716 364165 166569 613910 548375 854056 976363 459488 838513 406906 973551 166505 345012 791892 066235 022055 799689 160665 388522 093444 128187 204496 080277 010698 271266 939586 255906 681512 912654 102591 716475 718314 632786 393400 967599 691402 168490 191328 321315 888383 412204 140348 725186 978784 693807 076544 006922 119839 322507 485009 374062 723996 551947 453953 385645 115506 326002 205721 113305 358646 845536 345840 176812 898500 736649 873267 553941 959671 191219 766441 790573 248198 891214 804076 664180 373677 733328 262862 369222 857222 569824 039928 353040 194949 603529 281197 011364 327319 249565 109799 778176 358333 355934 071327 923272 128594 013648 492126 965692 984046 339715 641331 816554 305275 762551 315526 219624 350737 035959 803304 585418 617562 924585 555881 667637 244191 382110 173372 571545 628363 888526 312598 653549 548097 589435 345593 580124 343875 279502 899636 060196 604857 963987 814433 731821 812568 945713 365398 058125 843665 837955 609210 185770 093416 019460 381192 791474 298628 756606 993784 477222 855182 605475 261780 889543 308164 765102 529082 021638 511639 445313 597402 424522 534354 015436 117722 218186 912217 768126 201392 976068 902587 982860 147752 582745 696364 135841 324199 134168 379633 033851 480084 340140 545997 691605 771217 389324 824378 270187 958277 110219 578265 845267 883058 924471 461991 000169 266768 177336 904954 616122 537847 911725 288122 011510 900114 545588 279734 099663 870609 915247 085069 402517 601949 234266 979519 473739 204254 451985 333501 138756 561075 824361 300794 507503 783580 725209 034543 705831 632872 068812 392854 109098 982980 145532 179474 197650 210410 365406 565366 076617 058679 410399 102756 116103 095840 885361 713136 047190 975060 848610 334443 760782 241939 015214 635205 791967 329594 443547 193745 513707 542423 007194 272820 190949 283967 722810 546408 575889 149622 139297 579587 165832 040262 970090 682177 882403 143162 989540 061282 035933 486284 488677 766903 618549 644007 930244 248140 554144 629693 738838 393782 534852 799547 602076 419439 146932 431682 118033 389348 353998 846716 194094 328725 576562 964872 501684 778373 787037 973453 845384 381932 946553 624726 365260 740581 995116 865766 034500 961892 127246 869372 763176 097346 002806 540446 586755 814852 963441 421251 245645 909691 597765 206928 400821 341271 679471 663644 461555 973117 981854 497642 421449 662285 420590 979336 009734 361809 020247 503972 758748 165424 136850 913076 707629 375723 871774 703275 807905 057690 734448 844789 079627 978789 875686 108489 878081 280443 912332 157851 965017 315919 460685 989965 909610 529808 568808 503829 952809 304832 122513 511011 206514 363920 559472 222612 468068 380931 654138 099314 650832 864873 071575 821359 562994 241425 275930 352738 526084 921409 224535 213089 843579 495784 871362 914306 699061 546918 817198 651928 331906 883947 112557 372451 239166 787122 298939 572973 091135 865668 371201 863421 505382 183578 197027 154475 618419 134526 900181 588963 918007 617516 575386 510113 434258 009676 436817 870438 899413 884783 273147 487783 033571 379803 796931 579187 722347 224394 054158 591197 140684 571128 455072 506856 299122 610903 721727 047303 796859 074373 300442 091051 005758 564151 186063 316802 302606 431475 373337 999078 176548 626086 610184 643475 433769 018405 508385 343182 525109 310914 546404 877362 186419 851619 432834 181868 382113 211016 727699 684141 560177 421636 128401 068517 796398 546902 779847 210556 617372 224935 143094 097499 685204 727584 299147 623900 824787 779888 465834 399547 886557 528840 767628 770432 442689 121030 876226 354353 337051 035571 557579 258094 509342 605950 831940 513343 961036 898355 423840 485651 508968 429223 598016 447829 798716 753988 033509 268067 / 3139 > 493169 [i]
- extracting embedded OOA [i] would yield OOA(493169, 1586, S49, 2, 3138), but
- m-reduction [i] would yield (31, 3169, 1586)-net in base 49, but
Mode: Bound (linear).
Optimality
Show details for fixed k and s, k and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
None.