Information on Result #1230616
Digital (63, 72, 6784758)-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, 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 (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 (10, 14, 195317)-net over F25, using
- net defined by OOA [i] based on linear OOA(2514, 195317, F25, 4, 4) (dual of [(195317, 4), 781254, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(2514, 390634, F25, 4) (dual of [390634, 390620, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(1) [i] based on
- linear OA(2513, 390625, F25, 4) (dual of [390625, 390612, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(255, 390625, F25, 2) (dual of [390625, 390620, 3]-code), using an extension Ce(1) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,1], and designed minimum distance d ≥ |I|+1 = 2 [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 Ce(3) ⊂ Ce(1) [i] based on
- OA 2-folding and stacking [i] based on linear OA(2514, 390634, F25, 4) (dual of [390634, 390620, 5]-code), using
- net defined by OOA [i] based on linear OOA(2514, 195317, F25, 4, 4) (dual of [(195317, 4), 781254, 5]-NRT-code), using
- digital (32, 41, 2097150)-net over F25, using
- net defined by OOA [i] based on linear OOA(2541, 2097150, F25, 9, 9) (dual of [(2097150, 9), 18874309, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(2541, 8388601, F25, 9) (dual of [8388601, 8388560, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(2541, large, F25, 9) (dual of [large, large−41, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 9765626 | 2510−1, 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(2541, large, F25, 9) (dual of [large, large−41, 10]-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(2541, 8388601, F25, 9) (dual of [8388601, 8388560, 10]-code), using
- net defined by OOA [i] based on linear OOA(2541, 2097150, F25, 9, 9) (dual of [(2097150, 9), 18874309, 10]-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.