Information on Result #1879184
There is no digital (182, 182+k, 564)-net over F4 for arbitrarily large k, because logical equivalence would yield (182, m, 564)-net in base 4 for arbitrarily large m, but
- m-reduction [i] would yield (182, 2814, 564)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(42814, 564, S4, 5, 2632), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 526116 431376 330127 423685 450765 972226 463382 089419 344270 130758 489833 262824 958533 174074 463025 689610 896254 103759 056507 976953 900288 163542 972724 346649 868943 214188 949535 807966 776356 479609 628909 888680 711968 146044 525749 150237 316240 500761 325550 652632 832644 200593 145158 580531 546162 375114 284484 399456 736186 002796 488168 127076 751444 675569 055642 374594 966429 948575 439408 037092 236065 692192 022149 983876 856386 173898 024323 823077 935397 959375 693099 487975 820391 919490 563543 070883 788922 842335 742637 744063 664563 992062 431464 510993 889798 780726 431524 121957 369342 162501 953092 188603 240961 717483 337450 556220 508192 351120 630804 020899 283154 762086 236109 698154 012157 104572 718118 836646 194906 748772 386809 978054 679291 957912 056934 579325 225822 856423 893835 885395 889209 051211 210216 747331 801018 372040 732627 879917 495640 693948 018136 443069 286842 013709 262588 475678 795123 545840 336539 592863 154757 182780 596909 562327 781252 886430 030915 872125 430919 390127 946074 242006 735006 133487 178613 107047 468201 726925 123722 927938 139828 690441 141416 084271 807328 710709 240460 571074 907195 824638 269818 308446 187166 411940 536467 214153 991396 510072 666250 750598 794546 762485 279472 421565 132896 613985 495037 095654 449176 086280 666807 446761 926607 479396 447111 445981 746505 835978 394922 350494 506626 988704 815497 736814 379355 662627 646075 987845 071345 830297 157823 931210 844097 475075 670297 538187 388013 019976 357023 189854 870183 823518 570006 888232 347481 609826 278119 964127 432680 411590 560945 548574 252053 268193 006960 302983 263790 401090 061601 662084 286935 819131 706083 071771 217594 779716 102010 461910 970325 747293 927469 021044 515882 036468 724204 186468 104725 636188 660985 991844 319270 637252 980166 531491 158841 331518 779380 943484 534938 131645 143289 515797 952363 868056 922036 319547 721294 249474 113870 235423 899495 872661 028864 / 2633 > 42814 [i]
- extracting embedded OOA [i] would yield OOA(42814, 564, S4, 5, 2632), 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.