Information on Result #3265330
Digital (64, 73, large)-net over F27, using 272 times duplication based on digital (62, 71, large)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 0, 265722)-net over F27, using
- s-reduction based on digital (0, 0, s)-net over F27 for arbitrarily large s, using
- digital (0, 0, 265722)-net over F27 (see above)
- digital (0, 0, 265722)-net over F27 (see above)
- digital (0, 0, 265722)-net over F27 (see above)
- digital (0, 0, 265722)-net over F27 (see above)
- digital (0, 0, 265722)-net over F27 (see above)
- digital (0, 0, 265722)-net over F27 (see above)
- digital (0, 0, 265722)-net over F27 (see above)
- digital (0, 0, 265722)-net over F27 (see above)
- digital (0, 0, 265722)-net over F27 (see above)
- digital (0, 0, 265722)-net over F27 (see above)
- digital (0, 0, 265722)-net over F27 (see above)
- digital (0, 0, 265722)-net over F27 (see above)
- digital (0, 0, 265722)-net over F27 (see above)
- digital (0, 0, 265722)-net over F27 (see above)
- digital (0, 0, 265722)-net over F27 (see above)
- digital (0, 0, 265722)-net over F27 (see above)
- digital (0, 0, 265722)-net over F27 (see above)
- digital (0, 1, 265722)-net over F27, using
- s-reduction based on digital (0, 1, s)-net over F27 for arbitrarily large s, using
- digital (0, 1, 265722)-net over F27 (see above)
- digital (0, 1, 265722)-net over F27 (see above)
- digital (0, 1, 265722)-net over F27 (see above)
- digital (0, 1, 265722)-net over F27 (see above)
- digital (3, 5, 265722)-net over F27, using
- s-reduction based on digital (3, 5, 551881)-net over F27, using
- digital (4, 7, 265722)-net over F27, using
- s-reduction based on digital (4, 7, 532899)-net over F27, using
- net defined by OOA [i] based on linear OOA(277, 532899, F27, 3, 3) (dual of [(532899, 3), 1598690, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(277, 532899, F27, 2, 3) (dual of [(532899, 2), 1065791, 4]-NRT-code), using
- net defined by OOA [i] based on linear OOA(277, 532899, F27, 3, 3) (dual of [(532899, 3), 1598690, 4]-NRT-code), using
- s-reduction based on digital (4, 7, 532899)-net over F27, 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 (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
- digital (0, 0, 265722)-net over F27, using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and t, m and t.
Other Results with Identical Parameters
None.
Depending Results
None.