Information on Result #1231948
Digital (89, 101, 3062680)-net over F27, using generalized (u, u+v)-construction based on
- digital (0, 2, 28)-net over F27, using
- digital (1, 4, 730)-net over F27, using
- net defined by OOA [i] based on linear OOA(274, 730, F27, 3, 3) (dual of [(730, 3), 2186, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(274, 730, F27, 2, 3) (dual of [(730, 2), 1456, 4]-NRT-code), using
- net defined by OOA [i] based on linear OOA(274, 730, F27, 3, 3) (dual of [(730, 3), 2186, 4]-NRT-code), using
- digital (9, 13, 265722)-net over F27, using
- net defined by OOA [i] based on linear OOA(2713, 265722, F27, 4, 4) (dual of [(265722, 4), 1062875, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(2713, 531444, F27, 4) (dual of [531444, 531431, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(2713, 531445, F27, 4) (dual of [531445, 531432, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- linear OA(2713, 531441, F27, 4) (dual of [531441, 531428, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(279, 531441, F27, 3) (dual of [531441, 531432, 4]-code or 531441-cap in PG(8,27)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 531440 = 274−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(270, 4, F27, 0) (dual of [4, 4, 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
- discarding factors / shortening the dual code based on linear OA(2713, 531445, F27, 4) (dual of [531445, 531432, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(2713, 531444, F27, 4) (dual of [531444, 531431, 5]-code), using
- net defined by OOA [i] based on linear OOA(2713, 265722, F27, 4, 4) (dual of [(265722, 4), 1062875, 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 (44, 56, 1398100)-net over F27, using
- net defined by OOA [i] based on linear OOA(2756, 1398100, F27, 12, 12) (dual of [(1398100, 12), 16777144, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(2756, 8388600, F27, 12) (dual of [8388600, 8388544, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(2756, large, F27, 12) (dual of [large, large−56, 13]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 275−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(2756, large, F27, 12) (dual of [large, large−56, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(2756, 8388600, F27, 12) (dual of [8388600, 8388544, 13]-code), using
- net defined by OOA [i] based on linear OOA(2756, 1398100, F27, 12, 12) (dual of [(1398100, 12), 16777144, 13]-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.