Information on Result #599523
There is no digital (53, 213, 220)-net over F4, because extracting embedded orthogonal array would yield linear OA(4213, 220, F4, 160) (dual of [220, 7, 161]-code), but
- residual code [i] would yield linear OA(453, 59, F4, 40) (dual of [59, 6, 41]-code), but
- residual code [i] would yield linear OA(413, 18, F4, 10) (dual of [18, 5, 11]-code), but
- “Liz†bound on codes from Brouwer’s database [i]
- residual code [i] would yield linear OA(413, 18, F4, 10) (dual of [18, 5, 11]-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
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No digital (53, 214, 220)-net over F4 | [i] | m-Reduction | |
| 2 | No digital (53, 215, 220)-net over F4 | [i] | ||
| 3 | No digital (53, 216, 220)-net over F4 | [i] | ||
| 4 | No digital (53, 217, 220)-net over F4 | [i] | ||
| 5 | No digital (53, 218, 220)-net over F4 | [i] | ||
| 6 | No digital (53, 219, 220)-net over F4 | [i] | ||
| 7 | No digital (53, 220, 220)-net over F4 | [i] | ||
| 8 | No digital (53, 221, 220)-net over F4 | [i] | ||
| 9 | No digital (53, 222, 220)-net over F4 | [i] | ||
| 10 | No digital (53, 223, 220)-net over F4 | [i] | ||
| 11 | No digital (53, 224, 220)-net over F4 | [i] | ||
| 12 | No digital (53, 225, 220)-net over F4 | [i] | ||
| 13 | No digital (53, 226, 220)-net over F4 | [i] | ||
| 14 | No digital (53, 227, 220)-net over F4 | [i] | ||
| 15 | No digital (53, 228, 220)-net over F4 | [i] | ||
| 16 | No digital (53, 229, 220)-net over F4 | [i] | ||
| 17 | No digital (53, 230, 220)-net over F4 | [i] | ||
| 18 | No digital (53, 231, 220)-net over F4 | [i] | ||
| 19 | No digital (53, 232, 220)-net over F4 | [i] | ||
| 20 | No digital (53, 233, 220)-net over F4 | [i] | ||
| 21 | No digital (53, 234, 220)-net over F4 | [i] | ||
| 22 | No digital (53, 235, 220)-net over F4 | [i] | ||
| 23 | No digital (53, 236, 220)-net over F4 | [i] | ||
| 24 | No digital (53, 237, 220)-net over F4 | [i] | ||
| 25 | No digital (53, 238, 220)-net over F4 | [i] | ||
| 26 | No digital (53, 239, 220)-net over F4 | [i] | ||
| 27 | No digital (53, 240, 220)-net over F4 | [i] | ||
| 28 | No digital (53, 241, 220)-net over F4 | [i] | ||
| 29 | No digital (53, 242, 220)-net over F4 | [i] | ||
| 30 | No digital (53, 243, 220)-net over F4 | [i] | ||
| 31 | No digital (53, 244, 220)-net over F4 | [i] | ||
| 32 | No digital (53, 245, 220)-net over F4 | [i] | ||
| 33 | No digital (53, 246, 220)-net over F4 | [i] | ||
| 34 | No digital (53, 247, 220)-net over F4 | [i] | ||
| 35 | No digital (53, 248, 220)-net over F4 | [i] | ||
| 36 | No digital (53, 249, 220)-net over F4 | [i] | ||
| 37 | No digital (53, 250, 220)-net over F4 | [i] | ||
| 38 | No digital (53, 251, 220)-net over F4 | [i] | ||
| 39 | No digital (53, 252, 220)-net over F4 | [i] | ||
| 40 | No digital (53, 253, 220)-net over F4 | [i] | ||
| 41 | No digital (53, 254, 220)-net over F4 | [i] | ||
| 42 | No digital (53, 255, 220)-net over F4 | [i] | ||
| 43 | No digital (53, 256, 220)-net over F4 | [i] | ||
| 44 | No digital (53, 257, 220)-net over F4 | [i] | ||
| 45 | No digital (53, 258, 220)-net over F4 | [i] | ||
| 46 | No digital (53, 259, 220)-net over F4 | [i] | ||
| 47 | No digital (53, 260, 220)-net over F4 | [i] | ||