MinT - Information on Result #1231076

Information on Result #1231076

Digital (37, 44, 5593702)-net over F₂₅, using generalized (u,Â 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
  - construction for strength kÂ =Â 1 [i]
digital (1, 3, 651)-net over F₂₅, using
- kÂ =Â 2 construction [i]
digital (6, 9, 2796200)-net over F₂₅, using
- s-reduction based on digital (6, 9, large)-net over F₂₅, using
  - net defined by OOA [i] based on linear OOA(25⁹, large, F₂₅, 3, 3), using
    - appending kth column [i] based on linear OOA(25⁹, large, F₂₅, 2, 3), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(25⁹, large, F₂₅, 3) (dual of [large, large−9, 4]-code), using
        product of projective cap with (hyper)oval [i] based on linear OA(25⁷, 391875, F₂₅, 3) (dual of [391875, 391868, 4]-code or 391875-cap in PG(6,25)), using
        product of two caps with tangent hyperplane [i]
digital (24, 31, 2796200)-net over F₂₅, using
- net defined by OOA [i] based on linear OOA(25³¹, 2796200, F₂₅, 7, 7) (dual of [(2796200, 7), 19573369, 8]-NRT-code), using
  - OOA 3-folding and stacking with additional row [i] based on linear OA(25³¹, 8388601, F₂₅, 7) (dual of [8388601, 8388570, 8]-code), using
    - discarding factors / shortening the dual code based on linear OA(25³¹, large, F₂₅, 7) (dual of [large, large−31, 8]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 9765626Â | 25¹⁰âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (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.