Information on Result #3241209
Digital (56, 59, large)-net over F27, using t-expansion based on digital (55, 59, large)-net over F27, using
- 4 times m-reduction [i] based on digital (55, 63, 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, 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 (3, 5, 265722)-net over F27, using
- s-reduction based on digital (3, 5, 551881)-net over F27, using
- digital (3, 5, 265722)-net over F27 (see above)
- 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 (28, 36, 2097150)-net over F27, using
- net defined by OOA [i] based on linear OOA(2736, 2097150, F27, 8, 8) (dual of [(2097150, 8), 16777164, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(2736, 8388600, F27, 8) (dual of [8388600, 8388564, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(2736, large, F27, 8) (dual of [large, large−36, 9]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 275−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(2736, large, F27, 8) (dual of [large, large−36, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(2736, 8388600, F27, 8) (dual of [8388600, 8388564, 9]-code), using
- net defined by OOA [i] based on linear OOA(2736, 2097150, F27, 8, 8) (dual of [(2097150, 8), 16777164, 9]-NRT-code), using
- digital (0, 0, 265722)-net over F27, using
- generalized (u, u+v)-construction [i] based on
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.