MinT - Information on Result #1232500

Information on Result #1232500

Digital (39, 46, 6696162)-net over F₂₇, using generalized (u,Â u+v)-construction based on

digital (0, 1, 551881)-net over F₂₇, using
- s-reduction based on digital (0, 1, s)-net over F₂₇ for arbitrarily large s, using
  - construction for strength kÂ =Â 1 [i]
digital (3, 5, 551881)-net over F₂₇, using
- kÂ =Â 2 construction [i]
digital (6, 9, 2796200)-net over F₂₇, using
- s-reduction based on digital (6, 9, large)-net over F₂₇, using
  - net defined by OOA [i] based on linear OOA(27⁹, large, F₂₇, 3, 3), using
    - appending kth column [i] based on linear OOA(27⁹, large, F₂₇, 2, 3), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(27⁹, large, F₂₇, 3) (dual of [large, large−9, 4]-code), using
        product of projective cap with (hyper)oval [i] based on linear OA(27⁷, 532899, F₂₇, 3) (dual of [532899, 532892, 4]-code or 532899-cap in PG(6,27)), using
        product of two caps with tangent hyperplane [i]
digital (24, 31, 2796200)-net over F₂₇, using
- net defined by OOA [i] based on linear OOA(27³¹, 2796200, F₂₇, 7, 7) (dual of [(2796200, 7), 19573369, 8]-NRT-code), using
  - OOA 3-folding and stacking with additional row [i] based on linear OA(27³¹, 8388601, F₂₇, 7) (dual of [8388601, 8388570, 8]-code), using
    - discarding factors / shortening the dual code based on linear OA(27³¹, large, F₂₇, 7) (dual of [large, large−31, 8]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 27¹⁰âˆ’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.