Information on Result #1840919
(22, 37, 586)-net in base 32, using net defined by OOA based on OOA(3237, 586, S32, 15, 15), using
- OOA 7-folding and stacking with additional row [i] based on OA(3237, 4103, S32, 15), using
- 1 times code embedding in larger space [i] based on OA(3236, 4102, S32, 15), using
- discarding parts of the base [i] based on linear OA(6430, 4102, F64, 15) (dual of [4102, 4072, 16]-code), using
- construction X applied to C([0,7]) ⊂ C([0,6]) [i] based on
- linear OA(6429, 4097, F64, 15) (dual of [4097, 4068, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(6425, 4097, F64, 13) (dual of [4097, 4072, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(641, 5, F64, 1) (dual of [5, 4, 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([0,7]) ⊂ C([0,6]) [i] based on
- discarding parts of the base [i] based on linear OA(6430, 4102, F64, 15) (dual of [4102, 4072, 16]-code), using
- 1 times code embedding in larger space [i] based on OA(3236, 4102, S32, 15), 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 | (23, 37, 586)-net in base 32 | [i] | t-Expansion | |
| 2 | (23, 38, 586)-net in base 32 | [i] | Net Duplication | |
| 3 | (24, 39, 586)-net in base 32 | [i] | ||