Information on Result #1198354
Digital (45, 68, 1790)-net over F27, using net defined by OOA based on linear OOA(2768, 1790, F27, 23, 23) (dual of [(1790, 23), 41102, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(2768, 19691, F27, 23) (dual of [19691, 19623, 24]-code), using
- construction X applied to C([0,11]) ⊂ C([0,10]) [i] based on
- linear OA(2767, 19684, F27, 23) (dual of [19684, 19617, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 276−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(2761, 19684, F27, 21) (dual of [19684, 19623, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 276−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(271, 7, F27, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(271, s, F27, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,11]) ⊂ C([0,10]) [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 (46, 69, 1790)-net over F27 | [i] | Net Duplication | |
| 2 | Digital (47, 70, 1790)-net over F27 | [i] | ||
| 3 | Digital (45, 67, 1790)-net over F27 | [i] | m-Reduction | |
| 4 | (61, 84, 1890)-net in base 27 | [i] | (u, u+v)-Construction for Nets | |
| 5 | (63, 86, 1906)-net in base 27 | [i] | ||
| 6 | (65, 88, 1940)-net in base 27 | [i] | ||