Information on Result #598974
There is no digital (23, 68, 80)-net over F3, because extracting embedded orthogonal array would yield linear OA(368, 80, F3, 45) (dual of [80, 12, 46]-code), but
- construction Y1 [i] would yield
- linear OA(367, 74, F3, 45) (dual of [74, 7, 46]-code), but
- residual code [i] would yield linear OA(322, 28, F3, 15) (dual of [28, 6, 16]-code), but
- “HHM†bound on codes from Brouwer’s database [i]
- residual code [i] would yield linear OA(322, 28, F3, 15) (dual of [28, 6, 16]-code), but
- OA(312, 80, S3, 6), but
- discarding factors would yield OA(312, 75, S3, 6), but
- the Rao or (dual) Hamming bound shows that M ≥ 551451 > 312 [i]
- discarding factors would yield OA(312, 75, S3, 6), but
- linear OA(367, 74, F3, 45) (dual of [74, 7, 46]-code), 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.