Information on Result #1871994
There is no (12, 12+k, 430)-net in base 32 for arbitrarily large k, because logical equivalence would yield (12, m, 430)-net in base 32 for arbitrarily large m, but
- m-reduction [i] would yield (12, 428, 430)-net in base 32, but
- extracting embedded OOA [i] would yield OA(32428, 430, S32, 416), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 71691 676251 784281 254058 400484 075409 501874 991245 269550 147151 117159 768863 342967 863999 956680 260873 011401 584750 328933 560737 799729 852488 274483 725974 897378 118480 425193 195847 102877 587530 921479 367026 937052 413301 638755 428086 300478 790203 611763 264069 102681 253057 202163 182306 159591 886501 383071 038897 901039 082677 790817 536968 819217 699159 641875 841788 462718 575571 478803 426264 705970 132015 268696 819131 963426 565070 095017 861575 490923 711780 361525 531750 110184 809732 895467 903442 403470 108735 096387 149570 892086 760998 701072 408698 960629 430594 290697 765813 264309 666588 106642 855005 806725 717311 638709 843627 011426 406465 180882 385843 781016 064075 033641 392951 919804 495027 534611 611648 / 417 > 32428 [i]
- extracting embedded OOA [i] would yield OA(32428, 430, S32, 416), but
Mode: Bound.
Optimality
Show details for fixed k and s, k and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
None.