MinT - Information on Result #1186252

Information on Result #1186252

Digital (111, 123, 1398126)-net over F₄, using net defined by OOA based on linear OOA(4¹²³, 1398126, F₄, 15, 12) (dual of [(1398126, 15), 20971767, 13]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OOA(4¹²³, 2796253, F₄, 3, 12) (dual of [(2796253, 3), 8388636, 13]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(4¹⁵, 52, F₄, 3, 6) (dual of [(52, 3), 141, 7]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(4⁵, 41, F₄, 3, 3) (dual of [(41, 3), 118, 4]-NRT-code), using
        appending kth column [i] based on linear OOA(4⁵, 41, F₄, 2, 3) (dual of [(41, 2), 77, 4]-NRT-code), using
        OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(4⁵, 41, F₄, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
        a cap found by Tallinii [i]
      2. linear OOA(4¹⁰, 26, F₄, 3, 6) (dual of [(26, 3), 68, 7]-NRT-code), using
        extracting embedded OOA [i] based on digital (4, 10, 26)-net over F₄, using
        linear code embedding found in a computer search [i]
  2. linear OOA(4¹⁰⁸, 2796201, F₄, 3, 12) (dual of [(2796201, 3), 8388495, 13]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(4¹⁰⁸, large, F₄, 12) (dual of [large, large−108, 13]-code), using
      - the primitive narrow-sense BCH-code C(I) with length 16777215Â = 4¹²âˆ’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.