MinT - Information on Result #1188258

Information on Result #1188258

Digital (51, 58, 2796875)-net over F₅, using net defined by OOA based on linear OOA(5⁵⁸, 2796875, F₅, 9, 7) (dual of [(2796875, 9), 25171817, 8]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(5⁵⁸, 2796876, F₅, 3, 7) (dual of [(2796876, 3), 8390570, 8]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(5⁷, 675, F₅, 3, 3) (dual of [(675, 3), 2018, 4]-NRT-code), using
    - appending kth column [i] based on linear OOA(5⁷, 675, F₅, 2, 3) (dual of [(675, 2), 1343, 4]-NRT-code), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(5⁷, 675, F₅, 3) (dual of [675, 668, 4]-code or 675-cap in PG(6,5)), using
        product of two caps with tangent hyperplane [i]
  2. linear OOA(5⁵¹, 2796201, F₅, 3, 7) (dual of [(2796201, 3), 8388552, 8]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(5⁵¹, large, F₅, 7) (dual of [large, large−51, 8]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 9765624Â = 5¹⁰âˆ’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.