Information on Result #1879790
There is no digital (73, 73+k, 461)-net over F7 for arbitrarily large k, because logical equivalence would yield (73, m, 461)-net in base 7 for arbitrarily large m, but
- m-reduction [i] would yield (73, 1379, 461)-net in base 7, but
- extracting embedded OOA [i] would yield OOA(71379, 461, S7, 3, 1306), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 35928 700188 228810 299251 641919 482889 227215 703718 424711 483074 102954 951467 597236 682179 847182 610518 387736 490302 878618 656393 727685 980548 720331 117611 336357 548108 029538 116051 792778 600017 244988 776053 553672 490712 566890 903820 722888 036127 976364 312707 082710 457474 063921 473221 701986 935197 980230 479010 883975 768332 824200 114164 477444 714840 297241 263145 629020 036879 693125 283029 648364 878047 115480 787124 885510 918500 420060 936397 848108 983253 737409 988733 273195 759086 411748 504469 050919 610395 105177 966688 740450 563635 568107 598772 841197 096308 519659 606138 596567 009115 710189 496586 662948 291039 608843 349479 474935 747124 617201 569564 131688 581853 109363 238253 925154 501254 779849 218350 016450 220205 771178 113403 448447 181606 849437 601831 815375 979734 936857 262565 685521 802534 655432 602431 716512 112258 229747 993888 385085 918003 751222 353630 072429 795617 141967 677001 372469 755798 119718 136756 094441 719436 379690 685169 879950 607744 913899 054227 594152 297690 207426 500295 377640 619953 134898 022246 750263 173704 737604 947117 070873 127367 736170 167083 802375 238335 023558 751442 282616 138356 260690 032459 332792 103011 036226 163505 744475 315133 287263 170270 352296 475571 918745 540142 889222 086756 896982 642769 659600 486873 151190 151068 606035 324678 652209 / 1307 > 71379 [i]
- extracting embedded OOA [i] would yield OOA(71379, 461, S7, 3, 1306), 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.