MinT - Information on Result #1188858

Information on Result #1188858

Digital (136, 149, 2796222)-net over F₅, using net defined by OOA based on linear OOA(5¹⁴⁹, 2796222, F₅, 15, 13) (dual of [(2796222, 15), 41943181, 14]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OOA(5¹⁴⁹, 5592445, F₅, 3, 13) (dual of [(5592445, 3), 16777186, 14]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(5¹⁴⁹, 5592446, F₅, 3, 13) (dual of [(5592446, 3), 16777189, 14]-NRT-code), using
  - generalized (u,Â u+v)-construction [i] based on
    1. linear OOA(5⁷, 44, F₅, 3, 4) (dual of [(44, 3), 125, 5]-NRT-code), using
      - extracting embedded OOA [i] based on digital (3, 7, 44)-net over F₅, using
        linear code embedding found in a computer search [i]
    2. linear OOA(5⁴¹, 2796201, F₅, 3, 6) (dual of [(2796201, 3), 8388562, 7]-NRT-code), using
      - OOA 3-folding [i] based on linear OA(5⁴¹, large, F₅, 6) (dual of [large, large−41, 7]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 9765624Â = 5¹⁰âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
    3. linear OOA(5¹⁰¹, 2796201, F₅, 3, 13) (dual of [(2796201, 3), 8388502, 14]-NRT-code), using
      - OOA 3-folding [i] based on linear OA(5¹⁰¹, large, F₅, 13) (dual of [large, large−101, 14]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 9765626Â | 5²⁰âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]

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.