Information on Result #1840393
(45, 58, 43692)-net in base 16, using net defined by OOA based on OOA(1658, 43692, S16, 13, 13), using
- OOA 6-folding and stacking with additional row [i] based on OA(1658, 262153, S16, 13), using
- 1 times code embedding in larger space [i] based on OA(1657, 262152, S16, 13), using
- discarding parts of the base [i] based on linear OA(6438, 262152, F64, 13) (dual of [262152, 262114, 14]-code), using
- construction X applied to C([0,6]) ⊂ C([0,5]) [i] based on
- linear OA(6437, 262145, F64, 13) (dual of [262145, 262108, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 646−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(6431, 262145, F64, 11) (dual of [262145, 262114, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 646−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(641, 7, F64, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(641, s, F64, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,6]) ⊂ C([0,5]) [i] based on
- discarding parts of the base [i] based on linear OA(6438, 262152, F64, 13) (dual of [262152, 262114, 14]-code), using
- 1 times code embedding in larger space [i] based on OA(1657, 262152, S16, 13), 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 | (46, 59, 43692)-net in base 16 | [i] | Net Duplication | |