Information on Result #1878518
There is no digital (100, 100+k, 214)-net over F3 for arbitrarily large k, because logical equivalence would yield (100, m, 214)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (100, 1063, 214)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(31063, 214, S3, 5, 963), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 463036 464577 475094 533812 757732 749807 143780 453126 787908 250752 317387 965881 143543 342110 801120 239979 029046 544838 573400 621431 256634 980861 606339 462848 159591 468613 449122 405277 351651 903524 051741 560867 295023 970036 094944 944209 796045 821751 442769 284825 202678 798981 425914 363612 783698 426259 297011 690490 846308 772925 768968 819962 760902 430811 510593 974514 929682 747529 817350 014391 968967 046684 740969 448365 526708 910097 364352 559786 384734 996471 813653 400476 531428 998835 917318 419537 617380 200301 465076 728387 619585 925414 065269 984082 746662 / 241 > 31063 [i]
- extracting embedded OOA [i] would yield OOA(31063, 214, S3, 5, 963), 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.