Information on Result #1203766
Digital (34, 52, 233017)-net over F128, using net defined by OOA based on linear OOA(12852, 233017, F128, 18, 18) (dual of [(233017, 18), 4194254, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(12852, 2097153, F128, 18) (dual of [2097153, 2097101, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(12852, 2097155, F128, 18) (dual of [2097155, 2097103, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(16) [i] based on
- linear OA(12852, 2097152, F128, 18) (dual of [2097152, 2097100, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(12849, 2097152, F128, 17) (dual of [2097152, 2097103, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(1280, 3, F128, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(17) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(12852, 2097155, F128, 18) (dual of [2097155, 2097103, 19]-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 (35, 53, 233017)-net over F128 | [i] | Net Duplication | |
| 2 | Digital (43, 61, 233146)-net over F128 | [i] | (u, u+v)-Construction for Nets | |
| 3 | Digital (44, 62, 233167)-net over F128 | [i] | ||
| 4 | Digital (46, 64, 233209)-net over F128 | [i] | ||
| 5 | Digital (47, 65, 233275)-net over F128 | [i] | ||
| 6 | Digital (48, 66, 233296)-net over F128 | [i] | ||
| 7 | Digital (49, 67, 233317)-net over F128 | [i] | ||
| 8 | Digital (50, 68, 233403)-net over F128 | [i] | ||
| 9 | Digital (50, 68, 233404)-net over F128 | [i] | ||
| 10 | (73, 91, 233017)-net in base 16 | [i] | Base Change | |