Information on Result #1824584
(51, 84, 1025)-net in base 64, using base change based on digital (39, 72, 1025)-net over F128, using
- 1282 times duplication [i] based on digital (37, 70, 1025)-net over F128, using
- net defined by OOA [i] based on linear OOA(12870, 1025, F128, 33, 33) (dual of [(1025, 33), 33755, 34]-NRT-code), using
- OOA 16-folding and stacking with additional row [i] based on linear OA(12870, 16401, F128, 33) (dual of [16401, 16331, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(12870, 16402, F128, 33) (dual of [16402, 16332, 34]-code), using
- construction X applied to C([0,16]) ⊂ C([0,13]) [i] based on
- linear OA(12865, 16385, F128, 33) (dual of [16385, 16320, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(12853, 16385, F128, 27) (dual of [16385, 16332, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(1285, 17, F128, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,128)), using
- discarding factors / shortening the dual code based on linear OA(1285, 128, F128, 5) (dual of [128, 123, 6]-code or 128-arc in PG(4,128)), using
- Reed–Solomon code RS(123,128) [i]
- discarding factors / shortening the dual code based on linear OA(1285, 128, F128, 5) (dual of [128, 123, 6]-code or 128-arc in PG(4,128)), using
- construction X applied to C([0,16]) ⊂ C([0,13]) [i] based on
- discarding factors / shortening the dual code based on linear OA(12870, 16402, F128, 33) (dual of [16402, 16332, 34]-code), using
- OOA 16-folding and stacking with additional row [i] based on linear OA(12870, 16401, F128, 33) (dual of [16401, 16331, 34]-code), using
- net defined by OOA [i] based on linear OOA(12870, 1025, F128, 33, 33) (dual of [(1025, 33), 33755, 34]-NRT-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 | (52, 85, 1025)-net in base 64 | [i] | Net Duplication | |
| 2 | (53, 86, 1025)-net in base 64 | [i] | ||
| 3 | (51, 83, 1025)-net in base 64 | [i] | m-Reduction | |