Information on Result #1185714
Digital (24, 29, 131077)-net over F4, using net defined by OOA based on linear OOA(429, 131077, F4, 5, 5) (dual of [(131077, 5), 655356, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(429, 262155, F4, 5) (dual of [262155, 262126, 6]-code), using
- construction X4 applied to Ce(4) ⊂ Ce(2) [i] based on
- 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, 262144, F4, 3) (dual of [262144, 262125, 4]-code or 262144-cap in PG(18,4)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(410, 11, F4, 10) (dual of [11, 1, 11]-code or 11-arc in PG(9,4)), using
- dual of repetition code with length 11 [i]
- linear OA(41, 11, F4, 1) (dual of [11, 10, 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(4) ⊂ Ce(2) [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 (25, 30, 131077)-net over F4 | [i] | Net Duplication | |
| 2 | Digital (131, 141, 6841957)-net over F4 | [i] | (u, u+v)-Construction for Nets | |
| 3 | Digital (142, 153, 6841957)-net over F4 | [i] | ||