Information on Result #1230607
Digital (76, 86, 6365328)-net over F25, using generalized (u, u+v)-construction based on
- digital (0, 0, 195317)-net over F25, using
- s-reduction based on digital (0, 0, s)-net over F25 for arbitrarily large s, using
- digital (0, 0, 195317)-net over F25 (see above)
- digital (0, 0, 195317)-net over F25 (see above)
- digital (0, 0, 195317)-net over F25 (see above)
- digital (0, 0, 195317)-net over F25 (see above)
- digital (0, 0, 195317)-net over F25 (see above)
- digital (0, 0, 195317)-net over F25 (see above)
- digital (0, 0, 195317)-net over F25 (see above)
- digital (0, 0, 195317)-net over F25 (see above)
- digital (0, 0, 195317)-net over F25 (see above)
- digital (0, 0, 195317)-net over F25 (see above)
- digital (0, 0, 195317)-net over F25 (see above)
- digital (0, 0, 195317)-net over F25 (see above)
- digital (0, 0, 195317)-net over F25 (see above)
- digital (0, 0, 195317)-net over F25 (see above)
- digital (0, 1, 195317)-net over F25, using
- s-reduction based on digital (0, 1, s)-net over F25 for arbitrarily large s, using
- digital (0, 1, 195317)-net over F25 (see above)
- digital (0, 1, 195317)-net over F25 (see above)
- digital (0, 1, 195317)-net over F25 (see above)
- digital (0, 1, 195317)-net over F25 (see above)
- digital (3, 5, 195317)-net over F25, using
- s-reduction based on digital (3, 5, 406901)-net over F25, using
- digital (3, 5, 195317)-net over F25 (see above)
- digital (4, 7, 195317)-net over F25, using
- s-reduction based on digital (4, 7, 391875)-net over F25, using
- net defined by OOA [i] based on linear OOA(257, 391875, F25, 3, 3) (dual of [(391875, 3), 1175618, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(257, 391875, F25, 2, 3) (dual of [(391875, 2), 783743, 4]-NRT-code), using
- net defined by OOA [i] based on linear OOA(257, 391875, F25, 3, 3) (dual of [(391875, 3), 1175618, 4]-NRT-code), using
- s-reduction based on digital (4, 7, 391875)-net over F25, using
- digital (13, 18, 195317)-net over F25, using
- net defined by OOA [i] based on linear OOA(2518, 195317, F25, 5, 5) (dual of [(195317, 5), 976567, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(2518, 390635, F25, 5) (dual of [390635, 390617, 6]-code), using
- construction X applied to C([0,2]) ⊂ C([0,1]) [i] based on
- linear OA(2517, 390626, F25, 5) (dual of [390626, 390609, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626 | 258−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(259, 390626, F25, 3) (dual of [390626, 390617, 4]-code or 390626-cap in PG(8,25)), using the expurgated narrow-sense BCH-code C(I) with length 390626 | 258−1, defining interval I = [0,1], and minimum distance d ≥ |{−1,0,1}|+1 = 4 (BCH-bound) [i]
- linear OA(251, 9, F25, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(251, s, F25, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,2]) ⊂ C([0,1]) [i] based on
- OOA 2-folding and stacking with additional row [i] based on linear OA(2518, 390635, F25, 5) (dual of [390635, 390617, 6]-code), using
- net defined by OOA [i] based on linear OOA(2518, 195317, F25, 5, 5) (dual of [(195317, 5), 976567, 6]-NRT-code), using
- digital (36, 46, 1677720)-net over F25, using
- net defined by OOA [i] based on linear OOA(2546, 1677720, F25, 10, 10) (dual of [(1677720, 10), 16777154, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(2546, 8388600, F25, 10) (dual of [8388600, 8388554, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(2546, large, F25, 10) (dual of [large, large−46, 11]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 255−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(2546, large, F25, 10) (dual of [large, large−46, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(2546, 8388600, F25, 10) (dual of [8388600, 8388554, 11]-code), using
- net defined by OOA [i] based on linear OOA(2546, 1677720, F25, 10, 10) (dual of [(1677720, 10), 16777154, 11]-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.