Information on Result #598580
There is no digital (32, 64, 72)-net over F2, because extracting embedded orthogonal array would yield linear OA(264, 72, F2, 32) (dual of [72, 8, 33]-code), but
- adding a parity check bit [i] would yield linear OA(265, 73, F2, 33) (dual of [73, 8, 34]-code), but
- “BJV†bound on codes from Brouwer’s database [i]
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 (32, 65, 72)-net over F2 | [i] | m-Reduction | |
| 2 | No digital (32, 66, 72)-net over F2 | [i] | ||
| 3 | No digital (32, 67, 72)-net over F2 | [i] | ||
| 4 | No digital (32, 68, 72)-net over F2 | [i] | ||
| 5 | No digital (32, 69, 72)-net over F2 | [i] | ||
| 6 | No digital (32, 70, 72)-net over F2 | [i] | ||
| 7 | No digital (32, 71, 72)-net over F2 | [i] | ||
| 8 | No digital (32, 72, 72)-net over F2 | [i] | ||
| 9 | No digital (32, 73, 72)-net over F2 | [i] | ||
| 10 | No digital (32, 74, 72)-net over F2 | [i] | ||
| 11 | No digital (32, 75, 72)-net over F2 | [i] | ||