Information on Result #1194768
Digital (16, 21, 524290)-net over F16, using net defined by OOA based on linear OOA(1621, 524290, F16, 5, 5) (dual of [(524290, 5), 2621429, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(1621, 1048581, F16, 5) (dual of [1048581, 1048560, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- linear OA(1621, 1048576, F16, 5) (dual of [1048576, 1048555, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(1616, 1048576, F16, 4) (dual of [1048576, 1048560, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(160, 5, F16, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(4) ⊂ Ce(3) [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 (67, 77, 3879730)-net over F16 | [i] | (u, u+v)-Construction for Nets | |
| 2 | Digital (72, 83, 3879730)-net over F16 | [i] | ||
| 3 | (23, 28, 524290)-net in base 8 | [i] | Base Change | |