Information on Result #1875585
There is no digital (28, m, 248)-net over F9 with m > ∞, because logical equivalence would yield (28, 248)-sequence in base 9, but
- net from sequence [i] would yield (28, m, 249)-net in base 9 for arbitrarily large m, but
- m-reduction [i] would yield (28, 495, 249)-net in base 9, but
- extracting embedded OOA [i] would yield OOA(9495, 249, S9, 2, 467), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 335840 781253 062703 066213 295674 476544 725250 732294 911387 406625 099889 963063 899483 030925 361559 175585 038348 806019 838660 921189 846810 593431 036659 011670 661296 030501 963018 905959 030839 780016 962411 462897 239849 210008 024340 304102 257739 070033 642753 027021 555171 131049 765324 931534 914496 150753 034862 291271 011880 367554 777275 016579 932880 806353 256215 109055 501675 790925 266495 173230 099419 103330 754041 543132 529788 400889 241505 121278 791259 319937 027590 903415 548632 618460 603214 542024 125667 522456 651735 / 13 > 9495 [i]
- extracting embedded OOA [i] would yield OOA(9495, 249, S9, 2, 467), but
- m-reduction [i] would yield (28, 495, 249)-net in base 9, but
Mode: Bound (linear).
Optimality
Show details for fixed t and s.
Other Results with Identical Parameters
None.
Depending Results
None.