Information on Result #1748056
Digital (45, 78, 4106)-net over F128, using net defined by OOA based on linear OOA(12878, 4106, F128, 36, 33) (dual of [(4106, 36), 147738, 34]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OOA(12878, 16425, F128, 4, 33) (dual of [(16425, 4), 65622, 34]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(12878, 16426, F128, 4, 33) (dual of [(16426, 4), 65626, 34]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(12878, 16426, F128, 33) (dual of [16426, 16348, 34]-code), using
- construction X applied to C([0,16]) ⊂ C([0,9]) [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(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(12813, 41, F128, 13) (dual of [41, 28, 14]-code or 41-arc in PG(12,128)), using
- discarding factors / shortening the dual code based on linear OA(12813, 128, F128, 13) (dual of [128, 115, 14]-code or 128-arc in PG(12,128)), using
- Reed–Solomon code RS(115,128) [i]
- discarding factors / shortening the dual code based on linear OA(12813, 128, F128, 13) (dual of [128, 115, 14]-code or 128-arc in PG(12,128)), using
- construction X applied to C([0,16]) ⊂ C([0,9]) [i] based on
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(12878, 16426, F128, 33) (dual of [16426, 16348, 34]-code), using
- discarding factors / shortening the dual code based on linear OOA(12878, 16426, F128, 4, 33) (dual of [(16426, 4), 65626, 34]-NRT-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
None.