Information on Result #1880305
There is no digital (5, m, 55)-net over F9 with unbounded m, because logical equivalence would yield digital (5, m, 55)-net over F9 for arbitrarily large m, but
- m-reduction [i] would yield digital (5, 50, 55)-net over F9, but
- extracting embedded orthogonal array [i] would yield linear OA(950, 55, F9, 45) (dual of [55, 5, 46]-code), but
- construction Y1 [i] would yield
- OA(949, 51, S9, 45), but
- the (dual) Plotkin bound shows that M ≥ 1 546132 562196 033993 109383 389296 863818 106322 566003 / 23 > 949 [i]
- OA(95, 55, S9, 4), but
- discarding factors would yield OA(95, 44, S9, 4), but
- the Rao or (dual) Hamming bound shows that M ≥ 60897 > 95 [i]
- discarding factors would yield OA(95, 44, S9, 4), but
- OA(949, 51, S9, 45), but
- construction Y1 [i] would yield
- extracting embedded orthogonal array [i] would yield linear OA(950, 55, F9, 45) (dual of [55, 5, 46]-code), but
Mode: Bound (linear).
Optimality
Show details for fixed t and s.
Other Results with Identical Parameters
None.
Depending Results
None.