Information on Result #1231670
Digital (58, 67, 4214880)-net over F27, using generalized (u, u+v)-construction based on
- digital (0, 1, 28)-net over F27, using
- s-reduction based on digital (0, 1, s)-net over F27 for arbitrarily large s, using
- digital (0, 1, 28)-net over F27 (see above)
- digital (0, 2, 28)-net over F27, using
- digital (3, 6, 20496)-net over F27, using
- net defined by OOA [i] based on linear OOA(276, 20496, F27, 3, 3) (dual of [(20496, 3), 61482, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(276, 20496, F27, 2, 3) (dual of [(20496, 2), 40986, 4]-NRT-code), using
- net defined by OOA [i] based on linear OOA(276, 20496, F27, 3, 3) (dual of [(20496, 3), 61482, 4]-NRT-code), using
- digital (12, 16, 2097150)-net over F27, using
- s-reduction based on digital (12, 16, 4194301)-net over F27, using
- net defined by OOA [i] based on linear OOA(2716, 4194301, F27, 4, 4) (dual of [(4194301, 4), 16777188, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(2716, 8388602, F27, 4) (dual of [8388602, 8388586, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(2716, large, F27, 4) (dual of [large, large−16, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 275−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(2716, large, F27, 4) (dual of [large, large−16, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(2716, 8388602, F27, 4) (dual of [8388602, 8388586, 5]-code), using
- net defined by OOA [i] based on linear OOA(2716, 4194301, F27, 4, 4) (dual of [(4194301, 4), 16777188, 5]-NRT-code), using
- s-reduction based on digital (12, 16, 4194301)-net over F27, using
- digital (32, 41, 2097150)-net over F27, using
- net defined by OOA [i] based on linear OOA(2741, 2097150, F27, 9, 9) (dual of [(2097150, 9), 18874309, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(2741, 8388601, F27, 9) (dual of [8388601, 8388560, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(2741, large, F27, 9) (dual of [large, large−41, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 2710−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2741, large, F27, 9) (dual of [large, large−41, 10]-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(2741, 8388601, F27, 9) (dual of [8388601, 8388560, 10]-code), using
- net defined by OOA [i] based on linear OOA(2741, 2097150, F27, 9, 9) (dual of [(2097150, 9), 18874309, 10]-NRT-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
None.