MinT - Information on Result #1191066

Information on Result #1191066

Digital (45, 51, 5637575)-net over F₈, using net defined by OOA based on linear OOA(8⁵¹, 5637575, F₈, 9, 6) (dual of [(5637575, 9), 50738124, 7]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(8⁵¹, 5637576, F₈, 3, 6) (dual of [(5637576, 3), 16912677, 7]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(8⁹, 45174, F₈, 3, 3) (dual of [(45174, 3), 135513, 4]-NRT-code), using
    - appending kth column [i] based on linear OOA(8⁹, 45174, F₈, 2, 3) (dual of [(45174, 2), 90339, 4]-NRT-code), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(8⁹, 45174, F₈, 3) (dual of [45174, 45165, 4]-code or 45174-cap in PG(8,8)), using
        product of two caps with tangent hyperplane [i]
  2. linear OOA(8⁴², 5592402, F₈, 3, 6) (dual of [(5592402, 3), 16777164, 7]-NRT-code), using
    - trace code [i] based on linear OOA(64²¹, 2796201, F₆₄, 3, 6) (dual of [(2796201, 3), 8388582, 7]-NRT-code), using
      - OOA 3-folding [i] based on linear OA(64²¹, large, F₆₄, 6) (dual of [large, large−21, 7]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 64⁴âˆ’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.