Information on Result #1855287
There is no (25, m, 1691)-net in base 64 for arbitrarily large m, because m-reduction would yield (25, 1689, 1691)-net in base 64, but
- extracting embedded OOA [i] would yield OA(641689, 1691, S64, 1664), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 83421 364171 020209 904254 360111 596892 018783 984708 670267 869546 873774 434919 289376 648842 989792 807624 478338 506264 823488 385635 325468 751986 310083 059052 202114 047896 287923 510843 314329 441236 223167 472248 949330 425136 619594 525929 457389 966908 467602 841271 747499 640393 206026 914060 565537 776084 318338 549961 288443 552245 923984 634205 293444 493899 600078 541891 728241 891542 185753 382554 149633 025856 228949 015494 356069 819051 647610 995945 862675 978352 809129 652858 009352 712512 300695 836004 655104 440303 891309 501161 177699 188597 777773 477060 122138 137571 099093 914935 397147 435362 858528 555673 547420 067984 462173 511580 638174 188801 794156 746023 932279 380015 122426 354340 811184 815223 534976 073914 887775 393451 016859 962068 094026 743839 273590 553709 881940 459842 381808 055037 549867 859957 125301 824393 930175 812640 742217 603742 157887 037799 649651 767460 176303 988904 707557 740448 842109 571585 759253 817249 255173 238152 518159 273162 445895 112382 115232 673675 583085 962147 201005 267213 519245 177344 143042 329640 677675 611304 787801 603620 739591 449870 787341 834526 821058 619609 220126 917819 274831 251882 884867 615850 097116 543878 426788 028998 683114 651976 033488 291577 255389 319096 223802 740323 310590 871109 159379 051782 200988 451918 302213 265957 967757 113886 544411 516103 533827 717145 513797 355255 284479 059996 539326 533012 746725 426546 720883 901874 663264 960114 776360 324281 538925 604423 784663 381078 441816 362984 032514 393884 381361 643090 594897 153216 292003 425830 845066 412319 454345 057664 862618 035363 422506 757986 216007 361722 540203 590049 628823 564896 916875 636170 725258 442174 049725 695350 012424 111386 539355 423438 575044 005983 235021 869347 892827 578342 033045 313863 918750 317457 190477 458388 320926 917134 926066 964935 728805 414023 802678 843021 495543 322677 942778 153337 567165 472803 836443 776346 203910 544270 422089 689235 192482 512546 321099 284084 322613 280100 348513 139839 775408 704035 456607 920745 197130 247896 813934 309351 716580 542462 306453 220163 865820 105285 221406 185717 018807 171442 707125 459207 992643 421707 102523 309630 120471 847116 354764 330595 934966 545710 310251 010166 144747 053245 448521 008372 483122 796482 776610 386787 220366 516356 589566 667029 806789 511751 276119 947293 015131 411709 078552 958347 176778 971513 387393 401848 333240 909709 440174 182529 704642 165876 834168 453879 343442 265309 098137 991380 847148 455946 342735 468715 807317 907707 682781 550467 211671 182503 238554 438393 758365 487821 493868 834715 907939 955140 085723 132620 215448 185227 352521 339281 961666 289673 699694 031046 217470 450994 411422 064245 361079 499457 272510 409201 579933 800893 543593 815885 530507 558532 315368 048697 123534 589432 982324 075133 267731 155133 371548 245379 508800 530996 014551 462302 506386 260862 903461 187457 489225 633180 058293 427129 674307 241660 707645 693665 906944 062999 751120 453576 519108 744967 123503 272744 834940 540284 385962 282966 325421 668743 897607 208624 088136 466603 290675 715358 180803 798538 496401 134551 678777 080527 905796 343365 345171 203180 757346 212432 806839 414564 710910 563141 415648 307857 475932 487495 303916 850227 581264 349005 942319 784391 766596 523127 617058 125195 647865 770628 640471 552147 511775 867497 015535 160397 441884 738585 925411 788328 630518 620556 665845 216021 330307 810732 289250 821684 534369 039599 562397 817408 661892 985327 404534 877945 872599 709763 205364 274931 171328 / 185 > 641689 [i]
Mode: Bound.
Optimality
Show details for fixed m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No (25, 1690)-sequence in base 64 | [i] | Net from Sequence | |
| 2 | No (25, 25+k, 1691)-net in base 64 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (25, m, 1691)-net in base 64 with unbounded m | [i] | ||
| 4 | No digital (25, 25+k, 1691)-net over F64 for arbitrarily large k | [i] | ||
| 5 | No digital (25, m, 1691)-net over F64 with unbounded m | [i] | ||