Information on Result #3278201
(30, 50, 1639)-net in base 64, using t-expansion based on (29, 50, 1639)-net in base 64, using
- net defined by OOA [i] based on OOA(6450, 1639, S64, 21, 21), using
- OOA 10-folding and stacking with additional row [i] based on OA(6450, 16391, S64, 21), using
- 1 times code embedding in larger space [i] based on OA(6449, 16390, S64, 21), using
- discarding parts of the base [i] based on linear OA(12842, 16390, F128, 21) (dual of [16390, 16348, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,9]) [i] based on
- linear OA(12841, 16385, F128, 21) (dual of [16385, 16344, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(12837, 16385, F128, 19) (dual of [16385, 16348, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(1281, 5, F128, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,10]) ⊂ C([0,9]) [i] based on
- discarding parts of the base [i] based on linear OA(12842, 16390, F128, 21) (dual of [16390, 16348, 22]-code), using
- 1 times code embedding in larger space [i] based on OA(6449, 16390, S64, 21), using
- OOA 10-folding and stacking with additional row [i] based on OA(6450, 16391, S64, 21), 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 | (31, 51, 1639)-net in base 64 | [i] | Net Duplication | |