Information on Result #1878162
There is no digital (183, 183+k, 194)-net over F2 for arbitrarily large k, because logical equivalence would yield (183, m, 194)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (183, 1736, 194)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(21736, 194, S2, 9, 1553), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 3214 774872 016788 359853 256820 008932 250097 396875 711225 484474 210816 952308 417976 976541 100718 661394 211087 033655 282731 263884 249633 860602 029927 208513 309255 111755 149595 189179 042597 397257 178181 787900 252647 554583 825434 786278 703522 970602 760273 924592 310746 446765 384087 309547 308667 247800 239330 801819 710471 994016 211191 610302 941905 930872 451731 675704 251255 841142 697528 249624 381619 288938 418012 408854 062962 278812 687237 474269 845022 901066 546302 174037 441006 547869 329327 385332 363497 549595 968881 962494 517359 930034 138895 698244 044964 242379 038921 850880 / 777 > 21736 [i]
- extracting embedded OOA [i] would yield OOA(21736, 194, S2, 9, 1553), 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.