Information on Result #1878884
There is no digital (32, 32+k, 110)-net over F4 for arbitrarily large k, because logical equivalence would yield (32, m, 110)-net in base 4 for arbitrarily large m, but
- m-reduction [i] would yield (32, 435, 110)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(4435, 110, S4, 4, 403), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1 054875 063481 616124 677859 711331 326146 029316 510093 812405 543725 714230 154498 556273 149990 616921 915800 320772 623552 815563 309832 963862 612446 544498 079601 274639 873255 874571 437476 078886 965066 542754 190312 342423 904086 653876 992402 014005 611975 088780 301577 371103 880548 449901 346816 / 101 > 4435 [i]
- extracting embedded OOA [i] would yield OOA(4435, 110, S4, 4, 403), 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.