Information on Result #1878498
There is no digital (90, 90+k, 194)-net over F3 for arbitrarily large k, because logical equivalence would yield (90, m, 194)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (90, 963, 194)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3963, 194, S3, 5, 873), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1 929006 382495 839731 209283 500104 358490 732393 900396 991631 812486 135490 528650 498097 150349 040689 609013 923535 543241 427633 576472 971880 246892 947577 067239 247714 896939 147912 780399 590373 672855 567524 073429 569854 663386 533863 968261 082325 256624 481119 058130 088418 021931 676959 774167 919565 776446 943071 694464 159131 017513 090431 490808 124629 030137 989560 980404 257161 284953 662301 163523 314982 819564 613014 221212 172191 755110 323190 252736 669149 210780 630053 319651 348054 577265 947247 469371 774539 / 437 > 3963 [i]
- extracting embedded OOA [i] would yield OOA(3963, 194, S3, 5, 873), 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.