MinT - Information on Result #1183724

Information on Result #1183724

Digital (125, 137, 1398126)-net over F₃, using net defined by OOA based on linear OOA(3¹³⁷, 1398126, F₃, 15, 12) (dual of [(1398126, 15), 20971753, 13]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OOA(3¹³⁷, 2796253, F₃, 3, 12) (dual of [(2796253, 3), 8388622, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3¹³⁷, 2796254, F₃, 3, 12) (dual of [(2796254, 3), 8388625, 13]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(3¹⁷, 53, F₃, 3, 6) (dual of [(53, 3), 142, 7]-NRT-code), using
      - (u,Â u+v)-construction [i] based on
        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]
        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]
    2. linear OOA(3¹²⁰, 2796201, F₃, 3, 12) (dual of [(2796201, 3), 8388483, 13]-NRT-code), using
      - OOA 3-folding [i] based on linear OA(3¹²⁰, large, F₃, 12) (dual of [large, large−120, 13]-code), using
        the primitive narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [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.