Information on Result #1851012
There is no (73, m, 235)-net in base 4 for arbitrarily large m, because m-reduction would yield (73, 935, 235)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(4935, 235, S4, 4, 862), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 88 737590 369261 255992 365186 358546 747795 913204 644059 340265 573082 415584 944489 953958 101412 546314 138476 401657 433524 143096 951552 052041 137626 201706 830816 536157 100707 696452 917466 231780 371026 607499 834624 438819 668599 295477 969136 829983 289488 145215 996778 966991 287377 272759 859595 029205 455304 245338 573484 098791 936465 741704 340362 687004 559766 000220 310451 836643 689810 811102 811885 974473 313743 437329 237095 673307 114820 466619 738585 950107 797344 743438 685755 414562 352476 259357 858938 306514 761706 928804 814098 327533 782121 408066 643456 314485 923268 971639 838474 832865 590567 851760 913975 171558 146048 / 863 > 4935 [i]
Mode: Bound.
Optimality
Show details for fixed m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No (73, 234)-sequence in base 4 | [i] | Net from Sequence | |
| 2 | No (73, 73+k, 235)-net in base 4 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (73, m, 235)-net in base 4 with unbounded m | [i] | ||
| 4 | No digital (73, 73+k, 235)-net over F4 for arbitrarily large k | [i] | ||
| 5 | No digital (73, m, 235)-net over F4 with unbounded m | [i] | ||