Information on Result #3178659
Digital (23, 45, 5958)-net over F256, using 1 times m-reduction based on digital (23, 46, 5958)-net over F256, using
- net defined by OOA [i] based on linear OOA(25646, 5958, F256, 23, 23) (dual of [(5958, 23), 136988, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(25646, 65539, F256, 23) (dual of [65539, 65493, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(25646, 65542, F256, 23) (dual of [65542, 65496, 24]-code), using
- construction X applied to C([0,11]) ⊂ C([0,10]) [i] based on
- linear OA(25645, 65537, F256, 23) (dual of [65537, 65492, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(25641, 65537, F256, 21) (dual of [65537, 65496, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(2561, 5, F256, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, s, F256, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,11]) ⊂ C([0,10]) [i] based on
- discarding factors / shortening the dual code based on linear OA(25646, 65542, F256, 23) (dual of [65542, 65496, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(25646, 65539, F256, 23) (dual of [65539, 65493, 24]-code), using
Mode: Constructive and 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 | (50, 72, 5958)-net in base 32 | [i] | Base Change | |
| 2 | (38, 60, 5958)-net in base 64 | [i] | ||