MinT - Information on Result #1189802

Information on Result #1189802

Digital (39, 46, 274563)-net over F₇, using net defined by OOA based on linear OOA(7⁴⁶, 274563, F₇, 9, 7) (dual of [(274563, 9), 2471021, 8]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(7⁴⁶, 274564, F₇, 3, 7) (dual of [(274564, 3), 823646, 8]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(7⁴, 50, F₇, 3, 3) (dual of [(50, 3), 146, 4]-NRT-code), using
    - appending kth column [i] based on linear OOA(7⁴, 50, F₇, 2, 3) (dual of [(50, 2), 96, 4]-NRT-code), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(7⁴, 50, F₇, 3) (dual of [50, 46, 4]-code or 50-cap in PG(3,7)), using
        ovoid in PG(3,Â 7) [i]
  2. linear OOA(7⁴², 274514, F₇, 3, 7) (dual of [(274514, 3), 823500, 8]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(7⁴², 823542, F₇, 7) (dual of [823542, 823500, 8]-code), using
      - the primitive narrow-sense BCH-code C(I) with length 823542Â = 7⁷âˆ’1, defining interval IÂ =Â [1,7], 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.