Information on Result #1856277
There is no (4, m, 39)-net in base 7 for arbitrarily large m, because m-reduction would yield (4, 74, 39)-net in base 7, but
- extracting embedded OOA [i] would yield OOA(774, 39, S7, 2, 70), but
- the LP bound with quadratic polynomials shows that M ≥ 30665 141124 411175 854056 235783 580684 649065 396053 855752 734074 479561 / 71 > 774 [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 (4, 38)-sequence in base 7 | [i] | Net from Sequence | |
| 2 | No (4, 4+k, 39)-net in base 7 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (4, m, 39)-net in base 7 with unbounded m | [i] | ||