Information on Result #3265403
Digital (71, 82, 5033160)-net over F27, using 271 times duplication based on digital (70, 81, 5033160)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (6, 9, 1677720)-net over F27, using
- s-reduction based on digital (6, 9, large)-net over F27, using
- net defined by OOA [i] based on linear OOA(279, large, F27, 3, 3), using
- appending kth column [i] based on linear OOA(279, large, F27, 2, 3), using
- OAs with strength 3, b ≠ 2, and m > 3 are always embeddable [i] based on linear OA(279, large, F27, 3) (dual of [large, large−9, 4]-code), using
- appending kth column [i] based on linear OOA(279, large, F27, 2, 3), using
- net defined by OOA [i] based on linear OOA(279, large, F27, 3, 3), using
- s-reduction based on digital (6, 9, large)-net over F27, using
- digital (16, 21, 1677720)-net over F27, using
- s-reduction based on digital (16, 21, 4194301)-net over F27, using
- net defined by OOA [i] based on linear OOA(2721, 4194301, F27, 5, 5) (dual of [(4194301, 5), 20971484, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(2721, large, F27, 5) (dual of [large, large−21, 6]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 2710−1, 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(2721, large, F27, 5) (dual of [large, large−21, 6]-code), using
- net defined by OOA [i] based on linear OOA(2721, 4194301, F27, 5, 5) (dual of [(4194301, 5), 20971484, 6]-NRT-code), using
- s-reduction based on digital (16, 21, 4194301)-net over F27, using
- digital (40, 51, 1677720)-net over F27, using
- net defined by OOA [i] based on linear OOA(2751, 1677720, F27, 11, 11) (dual of [(1677720, 11), 18454869, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(2751, 8388601, F27, 11) (dual of [8388601, 8388550, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(2751, large, F27, 11) (dual of [large, large−51, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 2710−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2751, large, F27, 11) (dual of [large, large−51, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(2751, 8388601, F27, 11) (dual of [8388601, 8388550, 12]-code), using
- net defined by OOA [i] based on linear OOA(2751, 1677720, F27, 11, 11) (dual of [(1677720, 11), 18454869, 12]-NRT-code), using
- digital (6, 9, 1677720)-net over F27, 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.