Information on Result #1813476
Digital (19, 36, 6234)-net over F128, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(12836, 6234, F128, 2, 17) (dual of [(6234, 2), 12432, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(12836, 8198, F128, 2, 17) (dual of [(8198, 2), 16360, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(12836, 16396, F128, 17) (dual of [16396, 16360, 18]-code), using
- construction X applied to C([0,8]) ⊂ C([0,6]) [i] based on
- linear OA(12833, 16385, F128, 17) (dual of [16385, 16352, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(12825, 16385, F128, 13) (dual of [16385, 16360, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(1283, 11, F128, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,128) or 11-cap in PG(2,128)), using
- discarding factors / shortening the dual code based on linear OA(1283, 128, F128, 3) (dual of [128, 125, 4]-code or 128-arc in PG(2,128) or 128-cap in PG(2,128)), using
- Reed–Solomon code RS(125,128) [i]
- discarding factors / shortening the dual code based on linear OA(1283, 128, F128, 3) (dual of [128, 125, 4]-code or 128-arc in PG(2,128) or 128-cap in PG(2,128)), using
- construction X applied to C([0,8]) ⊂ C([0,6]) [i] based on
- OOA 2-folding [i] based on linear OA(12836, 16396, F128, 17) (dual of [16396, 16360, 18]-code), using
Mode: Linear.
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 | (25, 42, 6234)-net in base 64 | [i] | Base Change | |