Information on Result #1185704
Digital (18, 23, 8196)-net over F4, using net defined by OOA based on linear OOA(423, 8196, F4, 5, 5) (dual of [(8196, 5), 40957, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(423, 16393, F4, 5) (dual of [16393, 16370, 6]-code), using
- construction X4 applied to Ce(4) ⊂ Ce(2) [i] based on
- linear OA(422, 16384, F4, 5) (dual of [16384, 16362, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(415, 16384, F4, 3) (dual of [16384, 16369, 4]-code or 16384-cap in PG(14,4)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(48, 9, F4, 8) (dual of [9, 1, 9]-code or 9-arc in PG(7,4)), using
- dual of repetition code with length 9 [i]
- linear OA(41, 9, F4, 1) (dual of [9, 8, 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 (19, 24, 8196)-net over F4 | [i] | Net Duplication | |
| 2 | Digital (98, 108, 1685916)-net over F4 | [i] | (u, u+v)-Construction for Nets | |
| 3 | Digital (125, 135, 6719076)-net over F4 | [i] | ||
| 4 | Digital (109, 120, 1685916)-net over F4 | [i] | ||
| 5 | Digital (136, 147, 6719076)-net over F4 | [i] | ||