Information on Result #1880416
There is no digital (61, 61+k, 515)-net over F9 for arbitrarily large k, because logical equivalence would yield (61, m, 515)-net in base 9 for arbitrarily large m, but
- m-reduction [i] would yield (61, 1541, 515)-net in base 9, but
- extracting embedded OOA [i] would yield OOA(91541, 515, S9, 3, 1480), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 5782 236376 412504 998939 542816 916139 044388 844332 718129 841628 914247 409574 850810 935569 787364 272395 579073 502877 255679 279890 804399 095498 520104 637886 129787 823590 202549 885038 089894 098836 793440 006063 794261 649383 796446 274196 188767 548952 571696 604201 337348 047762 672403 113792 070728 886009 574257 663721 049643 972928 210119 340196 218704 212421 024106 569086 122706 559221 758742 572697 171216 015947 894876 057646 353646 082280 521562 069236 072047 097143 347394 978212 705703 261010 854843 137033 587164 028680 775636 466483 870783 581489 774641 987387 483404 837195 264271 269104 149456 313167 064552 767864 928305 837329 856202 614047 512079 493600 080507 980040 137212 597869 940394 278269 476586 256095 532555 632554 541672 992399 837956 092659 636195 748388 533613 259375 192283 209036 081815 061601 860982 970711 474713 004652 999806 485445 466651 239686 218521 663366 532629 905178 713285 718286 416163 132896 622615 185686 430737 059480 966601 726510 381647 204046 555162 036235 171222 010733 839672 330214 599837 218460 483404 897804 894025 109262 245471 295407 697311 498973 312833 661555 723211 907416 147613 896720 843197 359789 050624 927455 557196 307485 441892 588669 494131 047319 555887 481194 760918 070989 936899 026534 144125 755088 302252 449529 578402 407173 199600 672096 666981 849671 914766 294691 958748 072960 742224 264394 309175 704158 631773 658433 935044 957917 921461 083541 233318 877060 228020 406266 439504 901789 915372 293017 180801 248637 537819 078710 769576 150553 077189 169935 839044 504055 882809 694083 174524 215976 880794 193147 647861 700925 169444 465050 175363 667687 309327 160716 014279 186920 913441 852631 840446 605655 464167 227329 / 1481 > 91541 [i]
- extracting embedded OOA [i] would yield OOA(91541, 515, S9, 3, 1480), 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.