Information on Result #1231625
Digital (94, 107, 2815942)-net over F27, using generalized (u, u+v)-construction based on
- digital (0, 2, 28)-net over F27, using
- digital (0, 2, 28)-net over F27 (see above)
- digital (3, 6, 9843)-net over F27, using
- s-reduction based on 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
- s-reduction based on digital (3, 6, 20496)-net over F27, using
- digital (6, 10, 9843)-net over F27, using
- net defined by OOA [i] based on linear OOA(2710, 9843, F27, 4, 4) (dual of [(9843, 4), 39362, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(2710, 19686, F27, 4) (dual of [19686, 19676, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- linear OA(2710, 19683, F27, 4) (dual of [19683, 19673, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(277, 19683, F27, 3) (dual of [19683, 19676, 4]-code or 19683-cap in PG(6,27)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(270, 3, F27, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(270, s, F27, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- OA 2-folding and stacking [i] based on linear OA(2710, 19686, F27, 4) (dual of [19686, 19676, 5]-code), using
- net defined by OOA [i] based on linear OOA(2710, 9843, F27, 4, 4) (dual of [(9843, 4), 39362, 5]-NRT-code), using
- digital (20, 26, 1398100)-net over F27, using
- s-reduction based on digital (20, 26, 2796201)-net over F27, using
- net defined by OOA [i] based on linear OOA(2726, 2796201, F27, 6, 6) (dual of [(2796201, 6), 16777180, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(2726, large, F27, 6) (dual of [large, large−26, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 275−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- OA 3-folding and stacking [i] based on linear OA(2726, large, F27, 6) (dual of [large, large−26, 7]-code), using
- net defined by OOA [i] based on linear OOA(2726, 2796201, F27, 6, 6) (dual of [(2796201, 6), 16777180, 7]-NRT-code), using
- s-reduction based on digital (20, 26, 2796201)-net over F27, using
- digital (48, 61, 1398100)-net over F27, using
- net defined by OOA [i] based on linear OOA(2761, 1398100, F27, 13, 13) (dual of [(1398100, 13), 18175239, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(2761, 8388601, F27, 13) (dual of [8388601, 8388540, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(2761, large, F27, 13) (dual of [large, large−61, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 2710−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2761, large, F27, 13) (dual of [large, large−61, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(2761, 8388601, F27, 13) (dual of [8388601, 8388540, 14]-code), using
- net defined by OOA [i] based on linear OOA(2761, 1398100, F27, 13, 13) (dual of [(1398100, 13), 18175239, 14]-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.