Information on Result #1230822
Digital (61, 70, 5155004)-net over F25, using generalized (u, u+v)-construction based on
- digital (0, 1, 651)-net over F25, using
- s-reduction based on digital (0, 1, s)-net over F25 for arbitrarily large s, using
- digital (0, 1, 651)-net over F25 (see above)
- digital (1, 3, 651)-net over F25, using
- digital (5, 8, 958751)-net over F25, using
- net defined by OOA [i] based on linear OOA(258, 958751, F25, 3, 3) (dual of [(958751, 3), 2876245, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(258, 958751, F25, 2, 3) (dual of [(958751, 2), 1917494, 4]-NRT-code), using
- OAs with strength 3, b ≠ 2, and m > 3 are always embeddable [i] based on linear OA(258, 958751, F25, 3) (dual of [958751, 958743, 4]-code or 958751-cap in PG(7,25)), using
- appending kth column [i] based on linear OOA(258, 958751, F25, 2, 3) (dual of [(958751, 2), 1917494, 4]-NRT-code), using
- net defined by OOA [i] based on linear OOA(258, 958751, F25, 3, 3) (dual of [(958751, 3), 2876245, 4]-NRT-code), using
- digital (12, 16, 2097150)-net over F25, using
- s-reduction based on digital (12, 16, 4194301)-net over F25, using
- net defined by OOA [i] based on linear OOA(2516, 4194301, F25, 4, 4) (dual of [(4194301, 4), 16777188, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(2516, 8388602, F25, 4) (dual of [8388602, 8388586, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(2516, large, F25, 4) (dual of [large, large−16, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 255−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(2516, large, F25, 4) (dual of [large, large−16, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(2516, 8388602, F25, 4) (dual of [8388602, 8388586, 5]-code), using
- net defined by OOA [i] based on linear OOA(2516, 4194301, F25, 4, 4) (dual of [(4194301, 4), 16777188, 5]-NRT-code), using
- s-reduction based on digital (12, 16, 4194301)-net over F25, 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.