Information on Result #1879100
There is no digital (140, 140+k, 437)-net over F4 for arbitrarily large k, because logical equivalence would yield (140, m, 437)-net in base 4 for arbitrarily large m, but
- m-reduction [i] would yield (140, 2179, 437)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(42179, 437, S4, 5, 2039), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 692698 327339 341273 926657 734564 737608 345987 543572 756962 540226 356541 297142 394073 355604 637612 873174 201904 073401 827902 465234 166683 395823 377839 030712 438958 206417 212508 020822 630629 459565 269874 523343 983800 390092 685387 953908 371502 348057 289703 238944 652386 343403 983446 338443 045840 169492 186116 232027 080268 151190 310913 655745 589669 249378 851527 672383 496207 654358 908092 687326 342908 441248 716743 724315 097423 363371 921025 697593 529825 516907 809677 065418 851164 309007 600694 341165 624711 124441 653109 252153 873247 570306 551533 626413 959588 324979 437129 039655 411330 077029 788320 415856 420761 297113 645183 817536 966623 474219 613240 539821 815461 212831 425155 457724 103452 255615 516114 867460 896401 273623 821046 957784 397091 151545 370369 752034 208039 152194 723535 516974 905467 014354 678479 356005 736086 753441 872486 259797 720317 063166 671269 536570 762971 450195 120218 224532 555860 846575 376012 883871 912632 546745 824903 958529 962693 015040 998040 056872 590865 716132 189167 647757 751412 190637 191541 855501 144208 467079 816389 131933 130669 058469 164354 093435 502921 935582 729584 466717 448673 406740 464033 559760 524091 922361 803307 095434 148742 642172 351001 284585 525464 556737 862234 563066 790545 993127 812973 016386 700150 299881 093597 956499 820720 452645 386863 200495 041852 465486 375807 869942 527822 408307 694488 194866 124813 209350 249371 947964 034952 667653 473008 606909 578463 533712 823583 367664 708608 994037 465088 / 85 > 42179 [i]
- extracting embedded OOA [i] would yield OOA(42179, 437, S4, 5, 2039), 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.