MinT - Information on Result #1220864

Information on Result #1220864

Digital (33, 39, 5593654)-net over F₂₅, using (u,Â u+v)-construction 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, 30, 2796827)-net over F₂₅, using
- (u,Â u+v)-construction [i] based on
  1. digital (1, 4, 626)-net over F₂₅, using
    - net defined by OOA [i] based on linear OOA(25⁴, 626, F₂₅, 3, 3) (dual of [(626, 3), 1874, 4]-NRT-code), using
      - appending kth column [i] based on linear OOA(25⁴, 626, F₂₅, 2, 3) (dual of [(626, 2), 1248, 4]-NRT-code), using
        OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(25⁴, 626, F₂₅, 3) (dual of [626, 622, 4]-code or 626-cap in PG(3,25)), using
        ovoid in PG(3,Â 25) [i]
  2. digital (20, 26, 2796201)-net over F₂₅, using
    - net defined by OOA [i] based on linear OOA(25²⁶, 2796201, F₂₅, 6, 6) (dual of [(2796201, 6), 16777180, 7]-NRT-code), using
      - OA 3-folding and stacking [i] based on linear OA(25²⁶, large, F₂₅, 6) (dual of [large, large−26, 7]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 9765624Â = 25⁵âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [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.