Information on Result #1202726
Digital (24, 43, 731)-net over F81, using net defined by OOA based on linear OOA(8143, 731, F81, 19, 19) (dual of [(731, 19), 13846, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(8143, 6580, F81, 19) (dual of [6580, 6537, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(8143, 6581, F81, 19) (dual of [6581, 6538, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(11) [i] based on
- linear OA(8137, 6561, F81, 19) (dual of [6561, 6524, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(8123, 6561, F81, 12) (dual of [6561, 6538, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(816, 20, F81, 6) (dual of [20, 14, 7]-code or 20-arc in PG(5,81)), using
- discarding factors / shortening the dual code based on linear OA(816, 81, F81, 6) (dual of [81, 75, 7]-code or 81-arc in PG(5,81)), using
- Reed–Solomon code RS(75,81) [i]
- discarding factors / shortening the dual code based on linear OA(816, 81, F81, 6) (dual of [81, 75, 7]-code or 81-arc in PG(5,81)), using
- construction X applied to Ce(18) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(8143, 6581, F81, 19) (dual of [6581, 6538, 20]-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 (25, 43, 731)-net over F81 | [i] | t-Expansion | |
| 2 | Digital (25, 44, 731)-net over F81 | [i] | Net Duplication | |
| 3 | Digital (26, 45, 731)-net over F81 | [i] | ||
| 4 | Digital (24, 42, 731)-net over F81 | [i] | m-Reduction | |