MinT - Information on Result #3218323

Information on Result #3218323

Digital (222, 234, large)-net over F₄, using t-expansion based on digital (220, 234, large)-net over F₄, using

(u,Â u+v)-construction [i] based on
1. digital (67, 74, 5592400)-net over F₄, using
  - trace code for nets [i] based on digital (30, 37, 2796200)-net over F₁₆, using
    - net defined by OOA [i] based on linear OOA(16³⁷, 2796200, F₁₆, 7, 7) (dual of [(2796200, 7), 19573363, 8]-NRT-code), using
      - OOA 3-folding and stacking with additional row [i] based on linear OA(16³⁷, 8388601, F₁₆, 7) (dual of [8388601, 8388564, 8]-code), using
        discarding factors / shortening the dual code based on linear OA(16³⁷, large, F₁₆, 7) (dual of [large, large−37, 8]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 16¹²âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [i]
2. digital (146, 160, 4793484)-net over F₄, using
  - trace code for nets [i] based on digital (26, 40, 1198371)-net over F₂₅₆, using
    - net defined by OOA [i] based on linear OOA(256⁴⁰, 1198371, F₂₅₆, 14, 14) (dual of [(1198371, 14), 16777154, 15]-NRT-code), using
      - OA 7-folding and stacking [i] based on linear OA(256⁴⁰, 8388597, F₂₅₆, 14) (dual of [8388597, 8388557, 15]-code), using
        discarding factors / shortening the dual code based on linear OA(256⁴⁰, large, F₂₅₆, 14) (dual of [large, large−40, 15]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 256³âˆ’1, defining interval IÂ =Â [0,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [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		Method
1	Digital (223, 235, large)-net over F₄	[i]	Net Duplication
2	Digital (224, 236, large)-net over F₄	[i]
3	Digital (225, 237, large)-net over F₄	[i]
4	Digital (226, 238, large)-net over F₄	[i]
5	Digital (227, 239, large)-net over F₄	[i]
6	Digital (228, 240, large)-net over F₄	[i]
7	Digital (229, 241, large)-net over F₄	[i]
8	Digital (230, 242, large)-net over F₄	[i]