MinT - Information on Result #1218690

Information on Result #1218690

Digital (40, 47, 6781282)-net over F₁₆, using (u,Â u+v)-construction based on

digital (6, 9, 1188882)-net over F₁₆, using
- net defined by OOA [i] based on linear OOA(16⁹, 1188882, F₁₆, 3, 3) (dual of [(1188882, 3), 3566637, 4]-NRT-code), using
  - appending kth column [i] based on linear OOA(16⁹, 1188882, F₁₆, 2, 3) (dual of [(1188882, 2), 2377755, 4]-NRT-code), using
    - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(16⁹, 1188882, F₁₆, 3) (dual of [1188882, 1188873, 4]-code or 1188882-cap in PG(8,16)), using
      - product of two projective caps and (hyper)oval [i] based on
        linear OA(16⁴, 257, F₁₆, 3) (dual of [257, 253, 4]-code or 257-cap in PG(3,16)), using
        ovoid in PG(3,Â 16) [i]
        linear OA(16⁴, 257, F₁₆, 3) (dual of [257, 253, 4]-code or 257-cap in PG(3,16)) (see above)
digital (31, 38, 5592400)-net over F₁₆, using
- trace code for nets [i] based on digital (12, 19, 2796200)-net over F₂₅₆, using
  - net defined by OOA [i] based on linear OOA(256¹⁹, 2796200, F₂₅₆, 7, 7) (dual of [(2796200, 7), 19573381, 8]-NRT-code), using
    - appending kth column [i] based on linear OOA(256¹⁹, 2796200, F₂₅₆, 6, 7) (dual of [(2796200, 6), 16777181, 8]-NRT-code), using
      - OOA 3-folding and stacking with additional row [i] based on linear OA(256¹⁹, 8388601, F₂₅₆, 7) (dual of [8388601, 8388582, 8]-code), using
        discarding factors / shortening the dual code based on linear OA(256¹⁹, large, F₂₅₆, 7) (dual of [large, large−19, 8]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [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.