Information on Result #1882296
There is no digital (15, 15+k, 2065)-net over F128 for arbitrarily large k, because logical equivalence would yield (15, m, 2065)-net in base 128 for arbitrarily large m, but
- m-reduction [i] would yield (15, 2063, 2065)-net in base 128, but
- extracting embedded OOA [i] would yield OA(1282063, 2065, S128, 2048), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 3 249572 827619 171881 579858 843477 416975 235994 172028 295376 536377 903510 539396 881468 699979 735214 325412 929916 515156 241987 082407 050580 848930 134926 005840 143174 863519 383174 681984 580913 825764 644398 178485 590513 454322 936399 530869 669524 363418 579061 611565 342878 533852 766198 826995 340255 155865 032332 235860 848919 394151 179407 460953 898869 849366 784786 606058 166250 873208 436954 984438 425251 211203 552527 564609 644402 101828 522370 110164 593005 231554 155180 526058 206067 906740 703077 672764 426192 769373 812228 852160 061979 031162 307645 644742 125794 025009 811237 860948 064384 537683 126498 194376 478151 201981 921407 897100 779599 078665 276252 414999 404870 962921 724173 341981 318945 508664 404828 738065 128389 369419 335129 602970 293808 628623 389857 892916 348068 378266 024453 156409 802961 204198 068791 476164 377980 013250 265635 849978 335035 637032 698049 097064 679560 739062 785624 986057 651099 088394 487723 735519 245042 879764 277751 964466 147457 341127 873661 020136 827221 599698 841861 524404 790804 293469 086686 639845 965643 764313 539491 965605 154819 899288 587361 871559 312735 041235 386392 382878 459741 307032 096681 650051 207477 457098 220396 797292 896716 369308 715077 421424 331533 999738 343324 342286 430208 607360 551116 219078 389396 890557 608134 061856 866659 167446 238977 787547 658113 142990 741835 471544 807959 282160 700401 401731 980876 024111 711215 899167 866726 146165 369665 230182 704415 610564 482608 193415 625067 014419 478090 184193 666935 982011 751659 049048 321945 610509 808018 496589 709622 829134 838844 562633 628697 316721 802049 724230 455694 450232 407478 743362 920605 300954 126296 450495 575035 388261 719200 107818 317198 874639 120739 484615 639412 253606 064391 417468 765719 356090 719555 311554 601565 158985 046094 968403 352793 164834 612547 178042 743627 548548 249492 407908 387395 656449 063577 740498 618312 136627 392994 057358 898178 235851 710810 539340 220858 542406 131182 612783 298662 272035 496224 291400 801251 839042 352648 924228 573064 380069 558020 969512 474947 135375 666125 776260 216256 021479 705424 990141 737358 518406 048619 689106 224210 205651 237903 725062 115314 483072 008023 733103 676547 664752 122411 858826 087955 755564 767908 932441 913789 693514 232440 417281 014129 182553 216470 174043 253841 615049 887903 612561 859512 508448 647327 603290 946193 662257 394102 309361 453657 120000 138174 035457 273793 999852 113190 534228 241273 998087 149236 490322 721379 338337 441482 391872 764309 128956 884136 404059 540611 637155 924511 614663 414881 707594 148882 507934 742354 459135 954666 991352 859273 740175 752730 006719 256368 704691 353211 757811 189231 640476 236830 505523 292788 289583 395402 499528 806650 049398 003147 723518 505400 677290 914984 384907 838310 523607 280633 306289 392201 283166 410180 529882 781921 313710 511847 043525 041612 453229 616094 738165 974403 646518 975128 335315 563339 432205 045046 569678 684840 179750 710041 848726 211371 644740 113557 191272 948150 730019 977771 000070 388190 926505 419396 355080 068484 134096 576606 083882 835954 322117 974960 116748 362733 979021 745418 560206 705495 638100 485985 310537 686278 785174 019203 833384 635579 034216 265465 597843 247878 117827 830001 288600 014787 675614 327470 283117 843735 249555 342413 826490 533849 917108 417026 235038 226794 957373 625430 737605 086946 486386 516941 846640 676045 386241 174434 028855 065004 195958 810150 253627 306568 423930 776381 120748 858414 672413 199673 845908 885307 174811 904811 078508 889179 819955 572661 421949 767284 716316 031826 971872 254696 828918 494074 874971 649406 355096 979906 879151 390259 714373 995380 042979 145138 794823 294377 461194 673709 386443 234146 317024 948526 502105 296933 241155 445091 828280 608594 177904 193493 725391 546020 589755 771010 549999 761069 554804 247995 724157 434376 193167 937509 781688 257542 266445 533480 680916 731873 358529 982422 460188 946771 125838 094711 555412 979373 984720 017731 398038 458577 951380 791452 441428 773062 891564 628054 926660 433438 006295 139152 198443 258584 329812 229090 409515 290590 426724 989237 596062 181949 864750 221867 429057 670695 527468 111697 226074 659874 905516 821827 857665 607136 633834 946062 183980 767716 290527 288353 767413 119171 407804 050437 645692 652538 778125 497893 993695 134865 010490 814971 041840 298666 472727 524199 916786 583451 767946 971060 319725 296000 015090 588745 625512 177570 198398 563301 562800 445726 665874 634103 031822 077374 206575 448777 884675 998536 217383 924658 642937 815660 449531 412202 241954 674688 763141 354637 256269 729104 490428 352274 557510 974155 086994 203919 354408 150606 661154 557876 646187 467350 187723 831704 381209 497079 616469 254932 381906 083335 073837 976277 418250 308020 176588 453420 851086 805297 107706 056936 988049 296419 865180 232401 758499 704436 221945 854864 641558 258054 711742 784765 611322 389352 045470 214405 776571 031998 322376 646841 529840 080620 830147 315759 150260 979380 572129 329152 / 2049 > 1282063 [i]
- extracting embedded OOA [i] would yield OA(1282063, 2065, S128, 2048), 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.