Information on Result #599007
There is no digital (47, 127, 178)-net over F3, because extracting embedded orthogonal array would yield linear OA(3127, 178, F3, 80) (dual of [178, 51, 81]-code), but
- construction Y1 [i] would yield
- OA(3126, 150, S3, 80), but
- the linear programming bound shows that M ≥ 1 744284 668385 163500 346306 269658 104769 929699 691581 439318 970712 105752 702784 / 1 186440 433087 > 3126 [i]
- OA(351, 178, S3, 28), but
- discarding factors would yield OA(351, 172, S3, 28), but
- the Rao or (dual) Hamming bound shows that M ≥ 2 263924 665338 043697 613937 > 351 [i]
- discarding factors would yield OA(351, 172, S3, 28), but
- OA(3126, 150, S3, 80), but
Mode: Bound (linear).
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
None.