Information on Result #1878450
There is no digital (66, 66+k, 145)-net over F3 for arbitrarily large k, because logical equivalence would yield (66, m, 145)-net in base 3 for arbitrarily large m, but
- m-reduction [i] would yield (66, 719, 145)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3719, 145, S3, 5, 653), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1638 834127 452307 875008 132875 667903 661264 239096 104086 728675 639164 818834 226228 048527 597664 889413 237628 971896 648933 820436 349875 931068 151737 004859 300343 286309 261053 195923 154288 922188 058969 788023 222026 394939 469717 887665 047964 223136 888340 951072 970131 734458 866484 192802 931056 662184 412932 461024 201199 205585 763881 073015 551172 271654 195159 847466 582317 202182 / 109 > 3719 [i]
- extracting embedded OOA [i] would yield OOA(3719, 145, S3, 5, 653), 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.