Information on Result #1852653
There is no (94, m, 684)-net in base 8 for arbitrarily large m, because m-reduction would yield (94, 2048, 684)-net in base 8, but
- extracting embedded OOA [i] would yield OOA(82048, 684, S8, 3, 1954), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 72363 262785 164275 180449 558103 735581 183722 378568 675437 885732 374792 552176 811434 133990 098264 262141 258220 131443 256665 138977 691289 819698 786814 378358 105549 647992 421912 929650 477644 662937 120013 861028 040244 358385 378475 497764 958511 722910 573311 946254 566196 582580 896477 456205 764540 415839 056218 451437 727835 091107 067415 105517 099078 833316 404441 264433 364669 803778 993391 754969 820730 187915 837317 978411 803758 353415 583939 056061 968901 485756 372168 522666 965327 975283 019829 298185 218258 709834 097632 192955 563799 914073 008216 613026 325087 212396 964576 558615 677048 272770 576232 256693 930851 820105 926928 383546 722683 755396 074252 376163 481500 323440 635266 912790 085138 406799 818567 549199 738262 325597 545270 760651 795247 773572 535690 193010 766527 303623 356963 491755 104920 018809 096661 764503 447043 371256 730415 525051 363802 819815 811922 913659 658259 134421 673464 815563 163664 183408 290492 593571 610553 345516 246967 453381 700467 536358 185825 935451 624325 170260 662541 061730 241955 397754 820223 744428 288569 106777 952353 300392 792465 299675 742820 611137 448644 845125 275059 533713 304178 690881 133947 637018 036563 634466 997651 043332 161116 923632 769182 250450 816855 301157 684371 937391 828176 965950 669812 611492 136193 678824 488377 914424 234004 238731 373644 529847 065705 786772 593659 126707 251539 055831 916987 120264 060061 661258 968894 579426 951506 783003 216179 029010 368236 638996 544260 640395 329100 728505 901547 387637 943609 943236 702013 443556 111468 361095 499527 170623 720475 738362 901459 801296 470780 435512 946509 079848 189124 562859 924859 360290 960519 084637 979794 757719 071084 093000 951754 142035 927140 533049 341489 359238 437280 688845 029932 961902 283978 718744 055396 563366 494246 192593 081808 493444 160902 388796 073125 606989 153835 269595 092700 903049 416315 408160 919200 231212 737616 861768 833977 691707 079585 821284 311132 915284 938650 101913 998223 737082 413292 292706 382367 532766 362453 156216 585471 407820 394909 874422 409251 496718 828175 541506 502998 479550 349978 811404 107654 758509 051904 / 1955 > 82048 [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 (94, 683)-sequence in base 8 | [i] | Net from Sequence | |
| 2 | No (94, 94+k, 684)-net in base 8 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (94, m, 684)-net in base 8 with unbounded m | [i] | ||
| 4 | No digital (94, 94+k, 684)-net over F8 for arbitrarily large k | [i] | ||
| 5 | No digital (94, m, 684)-net over F8 with unbounded m | [i] | ||