Information on Result #1230566
Digital (86, 97, large)-net over F16, using generalized (u, u+v)-construction based on
- digital (7, 10, 3355440)-net over F16, using
- s-reduction based on digital (7, 10, large)-net over F16, using
- net defined by OOA [i] based on linear OOA(1610, large, F16, 3, 3), using
- appending kth column [i] based on linear OOA(1610, large, F16, 2, 3), using
- OAs with strength 3, b ≠ 2, and m > 3 are always embeddable [i] based on linear OA(1610, large, F16, 3) (dual of [large, large−10, 4]-code), using
- appending kth column [i] based on linear OOA(1610, large, F16, 2, 3), using
- net defined by OOA [i] based on linear OOA(1610, large, F16, 3, 3), using
- s-reduction based on digital (7, 10, large)-net over F16, using
- digital (20, 25, 3355440)-net over F16, using
- s-reduction based on digital (20, 25, 4194301)-net over F16, using
- net defined by OOA [i] based on linear OOA(1625, 4194301, F16, 5, 5) (dual of [(4194301, 5), 20971480, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(1625, large, F16, 5) (dual of [large, large−25, 6]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 1612−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- OOA 2-folding and stacking with additional row [i] based on linear OA(1625, large, F16, 5) (dual of [large, large−25, 6]-code), using
- net defined by OOA [i] based on linear OOA(1625, 4194301, F16, 5, 5) (dual of [(4194301, 5), 20971480, 6]-NRT-code), using
- s-reduction based on digital (20, 25, 4194301)-net over F16, using
- digital (51, 62, 3355440)-net over F16, using
- trace code for nets [i] based on digital (20, 31, 1677720)-net over F256, using
- net defined by OOA [i] based on linear OOA(25631, 1677720, F256, 11, 11) (dual of [(1677720, 11), 18454889, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(25631, 8388601, F256, 11) (dual of [8388601, 8388570, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(25631, large, F256, 11) (dual of [large, large−31, 12]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- discarding factors / shortening the dual code based on linear OA(25631, large, F256, 11) (dual of [large, large−31, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(25631, 8388601, F256, 11) (dual of [8388601, 8388570, 12]-code), using
- net defined by OOA [i] based on linear OOA(25631, 1677720, F256, 11, 11) (dual of [(1677720, 11), 18454889, 12]-NRT-code), using
- trace code for nets [i] based on digital (20, 31, 1677720)-net over F256, using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and t, m and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Digital (87, 97, large)-net over F16 | [i] | t-Expansion | |
| 2 | Digital (87, 98, large)-net over F16 | [i] | Net Duplication | |
| 3 | Digital (86, 96, large)-net over F16 | [i] | m-Reduction | |
| 4 | Digital (86, 95, large)-net over F16 | [i] | ||
| 5 | Digital (86, 94, large)-net over F16 | [i] | ||
| 6 | Digital (86, 93, large)-net over F16 | [i] | ||
| 7 | Digital (86, 92, large)-net over F16 | [i] | ||
| 8 | Digital (86, 91, large)-net over F16 | [i] | ||
| 9 | Digital (86, 90, large)-net over F16 | [i] | ||
| 10 | Digital (86, 89, large)-net over F16 | [i] | ||