Information on Result #1230613
Digital (74, 84, 4314763)-net over F25, using generalized (u, u+v)-construction based on
- digital (0, 0, 26)-net over F25, using
- s-reduction based on digital (0, 0, s)-net over F25 for arbitrarily large s, using
- digital (0, 0, 26)-net over F25 (see above)
- digital (0, 0, 26)-net over F25 (see above)
- digital (0, 0, 26)-net over F25 (see above)
- digital (0, 0, 26)-net over F25 (see above)
- digital (0, 0, 26)-net over F25 (see above)
- digital (0, 0, 26)-net over F25 (see above)
- digital (0, 0, 26)-net over F25 (see above)
- digital (0, 0, 26)-net over F25 (see above)
- digital (0, 0, 26)-net over F25 (see above)
- digital (0, 0, 26)-net over F25 (see above)
- digital (0, 0, 26)-net over F25 (see above)
- digital (0, 0, 26)-net over F25 (see above)
- digital (0, 0, 26)-net over F25 (see above)
- digital (0, 0, 26)-net over F25 (see above)
- digital (0, 1, 26)-net over F25, using
- s-reduction based on digital (0, 1, s)-net over F25 for arbitrarily large s, using
- digital (0, 1, 26)-net over F25 (see above)
- digital (0, 1, 26)-net over F25 (see above)
- digital (0, 1, 26)-net over F25 (see above)
- digital (0, 1, 26)-net over F25 (see above)
- digital (0, 2, 26)-net over F25, using
- digital (0, 2, 26)-net over F25 (see above)
- 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 (16, 21, 1677720)-net over F25, using
- s-reduction based on digital (16, 21, 4194301)-net over F25, using
- net defined by OOA [i] based on linear OOA(2521, 4194301, F25, 5, 5) (dual of [(4194301, 5), 20971484, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(2521, large, F25, 5) (dual of [large, large−21, 6]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 9765626 | 2510−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- OOA 2-folding and stacking with additional row [i] based on linear OA(2521, large, F25, 5) (dual of [large, large−21, 6]-code), using
- net defined by OOA [i] based on linear OOA(2521, 4194301, F25, 5, 5) (dual of [(4194301, 5), 20971484, 6]-NRT-code), using
- s-reduction based on digital (16, 21, 4194301)-net over F25, 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.