Information on Result #1858656
There is no (3, 1028)-sequence in base 256, because net from sequence would yield (3, m, 1029)-net in base 256 for arbitrarily large m, but
- m-reduction [i] would yield (3, 1027, 1029)-net in base 256, but
- extracting embedded OOA [i] would yield OA(2561027, 1029, S256, 1024), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 4684 727570 658364 119664 960173 694857 620580 561067 742665 489200 748526 025413 571645 530579 356424 134580 216622 921106 395965 223522 028652 363387 445702 478581 541757 525860 765691 753476 975621 554988 799328 658742 783072 396434 954540 915154 199665 472729 559490 370528 722322 326855 582293 095231 401713 573551 182752 470732 151231 881517 269399 246814 738830 884254 020711 982311 088049 693198 969251 364744 360599 730626 191782 659972 339738 529821 458991 999747 501066 678988 206592 935665 178373 387310 597713 517942 035620 245804 050691 900843 183108 203987 388071 335408 376570 222563 932870 683198 136054 136874 814766 476875 083110 200550 116058 920446 029942 528206 529363 582253 096263 576681 740137 495623 122443 585259 699853 111090 623255 384686 789069 078212 091926 387087 808159 681844 766553 193152 607295 995377 786351 144000 914920 555673 982849 489384 731779 555604 405723 688520 504496 410264 829080 970345 352219 362602 770795 643698 681050 055789 837613 892571 509348 721422 117696 234714 555854 903305 586643 592130 758649 864383 528993 716894 331380 213742 110250 060688 971135 856411 594141 082680 709646 605870 567809 044035 219177 066482 963908 117111 393788 213326 088361 009580 491616 804518 785578 186196 324275 735484 504771 080477 993529 334029 596658 737114 856530 002613 284084 748615 857682 913362 597623 441991 488841 629537 338018 413913 064392 377748 270629 577990 317434 241630 517391 812314 747453 679722 448073 370180 903111 019273 554534 242769 405360 453998 108533 177009 526525 671163 064839 032222 088501 604238 284653 850755 112123 304732 115719 833069 922586 624112 475176 651070 440926 380418 193997 270405 587705 873309 406727 348742 279700 301203 866817 819025 273780 139918 137240 823561 989383 713125 246006 670696 270714 440267 275395 730522 907453 696330 937016 443270 872595 956689 583138 185150 245193 233193 812601 346021 712409 682169 168269 981453 549017 131786 824421 998709 343732 821288 733688 625714 113096 156368 820435 267972 237323 735993 232417 552377 359969 927024 051360 345728 765044 230120 178422 773104 043191 035402 441744 385649 805962 013233 644936 354494 470990 996794 449830 321490 266958 713670 519203 156625 325865 137013 222970 312648 890325 052724 901039 732503 854766 670222 805484 901906 032343 724730 092668 345877 615358 013801 739808 408410 587336 635809 175666 694760 816878 693339 674701 725015 138830 661299 222621 064739 396163 391406 790658 110517 353296 588048 998003 001964 070934 521547 222008 716781 487358 160201 073334 777127 142299 507954 683168 870684 090098 298502 465378 143146 900299 497140 101459 614177 829152 596250 295192 220282 021183 717112 697454 692447 422225 056567 526254 188055 961030 610490 097020 960995 508327 888190 344736 895173 869679 813319 028991 890277 822160 488226 289588 511981 681320 632671 163849 100195 865933 448259 018085 845736 915612 679029 129216 / 205 > 2561027 [i]
- extracting embedded OOA [i] would yield OA(2561027, 1029, S256, 1024), but
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 (3, 1028)-sequence in base 256 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (3, m, 1028)-net in base 256 with m > ∞ | [i] | ||
| 3 | No digital (3, 1028)-sequence over F256 (for arbitrarily large k) | [i] | ||
| 4 | No digital (3, m, 1028)-net over F256 with m > ∞ | [i] | ||