Information on Result #1824029
(40, 55, 4682)-net in base 16, using base change based on digital (29, 44, 4682)-net over F32, using
- net defined by OOA [i] based on linear OOA(3244, 4682, F32, 15, 15) (dual of [(4682, 15), 70186, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(3244, 32775, F32, 15) (dual of [32775, 32731, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(3244, 32776, F32, 15) (dual of [32776, 32732, 16]-code), using
- construction X applied to C([0,7]) ⊂ C([0,6]) [i] based on
- linear OA(3243, 32769, F32, 15) (dual of [32769, 32726, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 326−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(3237, 32769, F32, 13) (dual of [32769, 32732, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 326−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(321, 7, F32, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(321, s, F32, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,7]) ⊂ C([0,6]) [i] based on
- discarding factors / shortening the dual code based on linear OA(3244, 32776, F32, 15) (dual of [32776, 32732, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(3244, 32775, F32, 15) (dual of [32775, 32731, 16]-code), using
Mode: Constructive.
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 | (41, 56, 4682)-net in base 16 | [i] | Net Duplication | |