MinT - Information on Result #1094592

Information on Result #1094592

Linear OOA(3¹⁷, 52, F₃, 5, 6) (dual of [(52, 5), 243, 7]-NRT-code), using OOA stacking with additional row based on linear OOA(3¹⁷, 53, F₃, 3, 6) (dual of [(53, 3), 142, 7]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(3⁵, 20, F₃, 3, 3) (dual of [(20, 3), 55, 4]-NRT-code), using
  - appending kth column [i] based on linear OOA(3⁵, 20, F₃, 2, 3) (dual of [(20, 2), 35, 4]-NRT-code), using
    - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(3⁵, 20, F₃, 3) (dual of [20, 15, 4]-code or 20-cap in PG(4,3)), using
      - doubling the cap [i] based on linear OA(3⁴, 10, F₃, 3) (dual of [10, 6, 4]-code or 10-cap in PG(3,3)), using
        ovoid in PG(3,Â 3) [i]
2. linear OOA(3¹², 33, F₃, 3, 6) (dual of [(33, 3), 87, 7]-NRT-code), using
  - extracting embedded OOA [i] based on digital (6, 12, 33)-net over F₃, using
    - linear code embedding found in a computer search [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

None.