Information on Result #1217560
Digital (127, 142, 2401119)-net over F9, using (u, u+v)-construction based on
- digital (21, 28, 4377)-net over F9, using
- net defined by OOA [i] based on linear OOA(928, 4377, F9, 7, 7) (dual of [(4377, 7), 30611, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(928, 13132, F9, 7) (dual of [13132, 13104, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(928, 13134, F9, 7) (dual of [13134, 13106, 8]-code), using
- trace code [i] based on linear OA(8114, 6567, F81, 7) (dual of [6567, 6553, 8]-code), using
- construction X applied to C([0,3]) ⊂ C([0,2]) [i] based on
- linear OA(8113, 6562, F81, 7) (dual of [6562, 6549, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(819, 6562, F81, 5) (dual of [6562, 6553, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(811, 5, F81, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(811, s, F81, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,3]) ⊂ C([0,2]) [i] based on
- trace code [i] based on linear OA(8114, 6567, F81, 7) (dual of [6567, 6553, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(928, 13134, F9, 7) (dual of [13134, 13106, 8]-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(928, 13132, F9, 7) (dual of [13132, 13104, 8]-code), using
- net defined by OOA [i] based on linear OOA(928, 4377, F9, 7, 7) (dual of [(4377, 7), 30611, 8]-NRT-code), using
- digital (99, 114, 2396742)-net over F9, using
- trace code for nets [i] based on digital (42, 57, 1198371)-net over F81, using
- net defined by OOA [i] based on linear OOA(8157, 1198371, F81, 15, 15) (dual of [(1198371, 15), 17975508, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(8157, 8388598, F81, 15) (dual of [8388598, 8388541, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(8157, large, F81, 15) (dual of [large, large−57, 16]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523361 | 818−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(8157, large, F81, 15) (dual of [large, large−57, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(8157, 8388598, F81, 15) (dual of [8388598, 8388541, 16]-code), using
- net defined by OOA [i] based on linear OOA(8157, 1198371, F81, 15, 15) (dual of [(1198371, 15), 17975508, 16]-NRT-code), using
- trace code for nets [i] based on digital (42, 57, 1198371)-net over F81, 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
None.