MinT - Information on Result #1232497

Information on Result #1232497

Digital (39, 46, 6531599)-net over F₂₇, using generalized (u,Â u+v)-construction based on

digital (0, 1, 1245133)-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 (4, 6, 1245133)-net over F₂₇, using
- s-reduction based on digital (4, 6, large)-net over F₂₇, using
  - kÂ =Â 2 construction [i]
digital (5, 8, 1245133)-net over F₂₇, using
- net defined by OOA [i] based on linear OOA(27⁸, 1245133, F₂₇, 3, 3) (dual of [(1245133, 3), 3735391, 4]-NRT-code), using
  - appending kth column [i] based on linear OOA(27⁸, 1245133, F₂₇, 2, 3) (dual of [(1245133, 2), 2490258, 4]-NRT-code), using
    - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(27⁸, 1245133, F₂₇, 3) (dual of [1245133, 1245125, 4]-code or 1245133-cap in PG(7,27)), using
      - product of projective cap with 27²-ovoid cap in AG(3,Â 27) [i] based on linear OA(27⁵, 1708, F₂₇, 3) (dual of [1708, 1703, 4]-code or 1708-cap in PG(4,27)), using
        large caps in PG(4,Â b) [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.