MinT - Information on Result #1210217

Information on Result #1210217

Digital (187, 200, 6990519)-net over F₄, using (u,Â u+v)-construction based on

digital (47, 53, 2796218)-net over F₄, using
- (u,Â u+v)-construction [i] based on
  1. digital (1, 4, 17)-net over F₄, using
    - net defined by OOA [i] based on linear OOA(4⁴, 17, F₄, 3, 3) (dual of [(17, 3), 47, 4]-NRT-code), using
      - appending kth column [i] based on linear OOA(4⁴, 17, F₄, 2, 3) (dual of [(17, 2), 30, 4]-NRT-code), using
        OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(4⁴, 17, F₄, 3) (dual of [17, 13, 4]-code or 17-cap in PG(3,4)), using
        ovoid in PG(3,Â 4) [i]
  2. digital (43, 49, 2796201)-net over F₄, using
    - net defined by OOA [i] based on linear OOA(4⁴⁹, 2796201, F₄, 6, 6) (dual of [(2796201, 6), 16777157, 7]-NRT-code), using
      - OA 3-folding and stacking [i] based on linear OA(4⁴⁹, large, F₄, 6) (dual of [large, large−49, 7]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 4¹²âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
digital (134, 147, 4194301)-net over F₄, using
- net defined by OOA [i] based on linear OOA(4¹⁴⁷, 4194301, F₄, 15, 13) (dual of [(4194301, 15), 62914368, 14]-NRT-code), using
  - OOA 2-folding and stacking with additional row [i] based on linear OOA(4¹⁴⁷, large, F₄, 3, 13), using
    - trace code [i] based on linear OOA(64⁴⁹, 2796201, F₆₄, 3, 13) (dual of [(2796201, 3), 8388554, 14]-NRT-code), using
      - OOA 3-folding [i] based on linear OA(64⁴⁹, large, F₆₄, 13) (dual of [large, large−49, 14]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [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.