Information on Result #1185854
Digital (41, 48, 87388)-net over F4, using net defined by OOA based on linear OOA(448, 87388, F4, 7, 7) (dual of [(87388, 7), 611668, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(448, 262165, F4, 7) (dual of [262165, 262117, 8]-code), using
- 1 times code embedding in larger space [i] based on linear OA(447, 262164, F4, 7) (dual of [262164, 262117, 8]-code), using
- construction X4 applied to Ce(6) ⊂ Ce(4) [i] based on
- linear OA(446, 262144, F4, 7) (dual of [262144, 262098, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(428, 262144, F4, 5) (dual of [262144, 262116, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(419, 20, F4, 19) (dual of [20, 1, 20]-code or 20-arc in PG(18,4)), using
- dual of repetition code with length 20 [i]
- linear OA(41, 20, F4, 1) (dual of [20, 19, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X4 applied to Ce(6) ⊂ Ce(4) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(447, 262164, F4, 7) (dual of [262164, 262117, 8]-code), using
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 (194, 208, 4880872)-net over F4 | [i] | (u, u+v)-Construction for Nets | |
| 2 | Digital (205, 220, 4880872)-net over F4 | [i] | ||