Information on Result #1194738
Digital (13, 17, 524294)-net over F16, using net defined by OOA based on linear OOA(1617, 524294, F16, 4, 4) (dual of [(524294, 4), 2097159, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(1617, 1048588, F16, 4) (dual of [1048588, 1048571, 5]-code), using
- construction X4 applied to Ce(3) ⊂ Ce(1) [i] based on
- linear OA(1616, 1048576, F16, 4) (dual of [1048576, 1048560, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(166, 1048576, F16, 2) (dual of [1048576, 1048570, 3]-code), using an extension Ce(1) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,1], and designed minimum distance d ≥ |I|+1 = 2 [i]
- linear OA(1611, 12, F16, 11) (dual of [12, 1, 12]-code or 12-arc in PG(10,16)), using
- dual of repetition code with length 12 [i]
- linear OA(161, 12, F16, 1) (dual of [12, 11, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(161, 16, F16, 1) (dual of [16, 15, 2]-code), using
- Reed–Solomon code RS(15,16) [i]
- discarding factors / shortening the dual code based on linear OA(161, 16, F16, 1) (dual of [16, 15, 2]-code), using
- construction X4 applied to Ce(3) ⊂ Ce(1) [i] based on
Mode: Constructive and 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 | Digital (53, 61, 4718594)-net over F16 | [i] | (u, u+v)-Construction for Nets | |
| 2 | Digital (58, 67, 4718594)-net over F16 | [i] | ||
| 3 | Digital (109, 122, 6116694)-net over F16 | [i] | Generalized (u, u+v)-Construction for Nets | |
| 4 | Digital (104, 116, 6116694)-net over F16 | [i] | ||