Information on Result #1879330
There is no digital (255, 255+k, 784)-net over F4 for arbitrarily large k, because logical equivalence would yield (255, m, 784)-net in base 4 for arbitrarily large m, but
- m-reduction [i] would yield (255, 3914, 784)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(43914, 784, S4, 5, 3659), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 10 682032 041171 844949 247665 697786 645822 710421 131232 167431 355930 531234 214218 195329 716370 123149 105196 057317 401155 098639 639247 222037 417492 986389 936533 377566 116062 657180 316961 197735 772278 534349 808547 915155 235510 992352 049323 323514 284759 837858 208835 694267 594697 730798 280373 510437 849238 893869 693311 688098 898403 706820 374448 254544 147781 337120 904917 521023 975997 706321 235850 289114 708222 645485 986854 760978 061679 634392 930414 484696 864683 653996 095674 456226 150110 091986 950370 066797 897268 824288 767762 928722 267254 869382 468290 826556 419020 051898 116341 696999 572792 381643 650377 584194 416559 995147 322110 077548 090999 445848 165558 867250 831176 827345 283716 492487 685281 964402 708721 275180 232588 159850 983119 871047 002381 551794 914388 517230 444589 487246 051534 683564 932768 190519 987525 310880 825376 960471 845676 977944 580321 391945 294713 444814 447290 746263 467845 537258 977973 217211 491870 035045 648392 147719 529764 997808 486525 104756 490930 112321 087724 876025 505761 468720 873597 981242 934389 295148 828718 466832 226727 768504 227350 023162 029200 161511 517769 132778 666550 155067 218530 214412 432914 760486 637066 590090 169470 903080 534341 338410 154618 458527 029498 768059 592691 955664 752398 006303 217707 323367 752328 972059 744909 296312 091065 450650 391382 461496 044553 733328 557973 662124 481066 226452 454340 330050 305204 468621 216417 524070 818500 091965 578629 806697 607105 290678 328556 879424 801612 000651 794865 532125 345811 575531 412634 897340 467468 318695 016431 051993 793251 957300 411706 691336 933597 697142 726415 606076 249530 491622 548557 193651 215084 343837 544277 648532 393661 713828 971733 454938 427167 442799 579689 770286 657003 248729 685219 755365 133573 647758 012434 446782 938735 998070 226976 753473 886411 966125 493313 455797 258121 932762 899315 710548 629991 978977 304295 352127 727067 035246 104592 495130 526840 143496 753665 595636 599966 654713 843107 473666 310112 002995 355482 170592 658986 068841 069739 631802 513301 753447 940492 566590 488933 082056 870905 420249 707720 889509 080037 228134 861555 798238 066405 124998 538178 521359 207190 264382 668831 773962 919734 796383 317107 872502 907628 712362 417404 988929 928872 267596 299897 157255 177518 312435 932776 806305 327372 244249 031310 329893 805599 204335 736379 275066 907176 713315 994184 065567 857869 994040 748700 038419 680877 855584 124705 142457 923454 869457 984791 274963 492537 488515 389535 256448 434968 034355 910405 625334 983408 639715 932060 572653 761129 303845 829181 765800 782939 771896 165993 064214 607622 779445 431472 484708 855323 831627 250783 351105 313685 988193 254514 546334 863938 551808 / 305 > 43914 [i]
- extracting embedded OOA [i] would yield OOA(43914, 784, S4, 5, 3659), 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.