Information on Result #1186466
Digital (87, 102, 37452)-net over F4, using net defined by OOA based on linear OOA(4102, 37452, F4, 15, 15) (dual of [(37452, 15), 561678, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(4102, 262165, F4, 15) (dual of [262165, 262063, 16]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4101, 262164, F4, 15) (dual of [262164, 262063, 16]-code), using
- construction X4 applied to Ce(14) ⊂ Ce(12) [i] based on
- linear OA(4100, 262144, F4, 15) (dual of [262144, 262044, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(482, 262144, F4, 13) (dual of [262144, 262062, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [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(14) ⊂ Ce(12) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(4101, 262164, F4, 15) (dual of [262164, 262063, 16]-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 (88, 103, 37452)-net over F4 | [i] | Net Duplication | |
| 2 | Digital (89, 104, 37452)-net over F4 | [i] | ||