Information on Result #1878526
There is no digital (104, 104+k, 222)-net over F3 for arbitrarily large k, because logical equivalence would yield (104, m, 222)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (104, 1103, 222)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(31103, 222, S3, 5, 999), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 5 463870 595451 600035 317870 592147 213241 843636 457594 577068 634460 317161 953254 807806 288319 013909 902764 268388 011939 560053 202720 274235 414418 956263 965712 559482 226547 213510 887952 241197 367602 205460 800921 146189 860860 022784 353342 668686 099212 474806 760359 713502 795333 946680 944822 067002 237172 085195 686165 853287 496261 298844 103338 227367 459563 697733 245306 134879 946300 658424 418022 707262 892407 151508 924345 847742 074515 605005 788288 410669 506058 450255 875114 207705 103826 024138 848020 949945 791156 356519 588046 158271 482181 360880 139428 969327 368889 248188 106019 / 250 > 31103 [i]
- extracting embedded OOA [i] would yield OOA(31103, 222, S3, 5, 999), 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.