MinT - Information on Result #3205900

Information on Result #3205900

Digital (80, 84, large)-net over F₄, using t-expansion based on digital (77, 84, large)-net over F₄, using

trace code for nets [i] based on digital (21, 28, 2796265)-net over F₆₄, using
- net defined by OOA [i] based on linear OOA(64²⁸, 2796265, F₆₄, 9, 7) (dual of [(2796265, 9), 25166357, 8]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OOA(64²⁸, 2796266, F₆₄, 3, 7) (dual of [(2796266, 3), 8388770, 8]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(64³, 65, F₆₄, 3, 3) (dual of [(65, 3), 192, 4]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(3;192,64) [i]
      2. linear OOA(64²⁵, 2796201, F₆₄, 3, 7) (dual of [(2796201, 3), 8388578, 8]-NRT-code), using
        OOA 3-folding [i] based on linear OA(64²⁵, large, F₆₄, 7) (dual of [large, large−25, 8]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [i]

Mode: Constructive and linear.

Optimality

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

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Digital (81, 85, large)-net over F₄	[i]		Net Duplication
2	Digital (82, 86, large)-net over F₄	[i]
3	Digital (83, 87, large)-net over F₄	[i]