Information on Result #1851324
There is no (177, m, 549)-net in base 4 for arbitrarily large m, because m-reduction would yield (177, 2739, 549)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(42739, 549, S4, 5, 2562), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 370 827757 126827 398478 900436 223629 556607 465813 847393 417638 520463 560549 851687 111531 877630 215720 614150 973423 324012 966152 083295 024548 800160 932932 631622 346431 464896 280853 712992 917211 115920 345617 953335 523246 301227 388535 867369 149198 043576 876580 418630 204220 442743 426984 273502 836327 178216 123775 673762 589065 778715 612053 600789 632919 232071 942707 152801 961835 693111 108618 748324 534056 740046 547929 546623 804995 162886 198917 074005 088733 150461 798815 723096 600140 367404 317301 007999 343450 990612 451423 147130 276800 803697 526986 840313 143441 239117 553602 183685 642083 630451 511633 617738 475088 394441 882129 032738 994125 632704 133873 215011 381874 530514 942346 112617 206804 164209 321075 511383 822331 044206 825015 337982 239318 016782 680021 576738 499420 650523 865348 700181 826794 601179 033470 501215 114327 000905 425759 200995 597470 989423 988465 351866 992182 183605 280759 443011 759769 988494 153664 565414 919082 222346 072333 040353 359936 515598 395225 288883 335421 819046 746505 759567 071484 852469 892376 017326 766973 425291 358034 682368 308564 194230 213857 603995 813651 877452 987222 002261 541474 932334 756053 757133 184436 535934 504905 089958 630163 761861 940915 780019 046435 293664 311681 498125 322702 169261 544061 017442 758902 489016 424181 286714 929487 398191 383658 164900 193742 306226 083628 246537 214335 243112 776581 658313 589208 739589 230947 033090 300469 796133 685064 031297 556108 837810 156166 673240 599409 372903 454036 578699 168214 985344 667878 377450 644533 900737 310514 858347 929952 227694 271318 291498 947248 176914 868378 680340 296255 655469 440731 015913 157491 050540 491581 760563 898980 831087 820534 598085 198826 331440 515564 253356 568175 510086 037793 522994 405796 995514 753159 912008 333264 162345 827799 351814 561309 225291 114021 976737 904899 049505 930239 232902 229238 691466 838016 / 2563 > 42739 [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 (177, 548)-sequence in base 4 | [i] | Net from Sequence | |
| 2 | No (177, 177+k, 549)-net in base 4 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (177, m, 549)-net in base 4 with unbounded m | [i] | ||
| 4 | No digital (177, 177+k, 549)-net over F4 for arbitrarily large k | [i] | ||
| 5 | No digital (177, m, 549)-net over F4 with unbounded m | [i] | ||